Details

analyze3.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
33.3%	25%	50%	0%	0%	25%	0%	3
75%	37.5%	12.5%	0%	12.5%	37.5%	0%	4
87.5%	43.7%	6.2%	0%	12.5%	37.5%	0%	5
93.8%	46.9%	3.1%	0%	12.5%	37.5%	0%	6
96.9%	48.4%	1.6%	0%	12.5%	37.5%	0%	7
98.4%	49.2%	0.8%	0%	12.5%	37.5%	0%	8
99.2%	49.6%	0.4%	0%	12.5%	37.5%	0%	9
99.6%	49.8%	0.2%	0%	12.5%	37.5%	0%	10
99.8%	49.9%	0.1%	0%	12.5%	37.5%	0%	11
99.9%	49.9%	0%	0%	12.5%	37.5%	0%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.8s (34%)

Results

1.2s	4973×	body	256	valid
1.1s	2033×	body	1024	valid
330.0ms	998×	body	512	valid
215.0ms	252×	body	2048	valid

Bogosity

preprocess22.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	33	8
5	50	8
6	87	8
7	123	8
8	170	8
9	206	8
10	232	8
11	234	8
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify11.0ms (0.1%)

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: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	33	8
5	50	8
6	87	8
7	123	8
8	170	8
9	206	8
10	232	8
11	234	8

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

Outputs
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
(-.f64 (log1p.f64 N) (log.f64 N))

eval1.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

27.8b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	27.8b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	2.7b	(-.f64 (log1p.f64 N) (log.f64 N))
✓	2.7b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	N	@	inf	(-.f64 (log1p.f64 N) (log.f64 N))
1.0ms	N	@	-inf	(-.f64 (log1p.f64 N) (log.f64 N))
1.0ms	N	@	0	(-.f64 (log1p.f64 N) (log.f64 N))

rewrite50.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

581×	`pow1_binary64`
541×	`add-log-exp_binary64`
541×	`expm1-log1p-u_binary64`
540×	`log1p-expm1-u_binary64`
529×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	106	8
2	1453	8

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(-.f64 (log1p.f64 N) (log.f64 N))

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

Outputs

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

simplify43.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
701×	`associate-l_binary64`
458×	`fma-neg_binary64`
427×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	192
1	95	188
2	237	185
3	646	181
4	2109	181

Stop Event

1×	node limit

Counts

47 → 50

Calls

Call 1

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

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

eval11.0ms (0.1%)

Compiler: Compiled 630 to 282 computations (55.2% saved)

prune52.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	7	51

Error

0.0b

Counts

51 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	34.2b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
▶	32.7b	(/.f64 1 N)
	28.2b	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
	29.0b	(-.f64 N (log.f64 N))
▶	29.9b	(neg.f64 (log.f64 N))
▶	27.7b	(log.f64 (/.f64 (+.f64 N 1) N))
▶	33.7b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))

Compiler

Compiled 114 to 78 computations (31.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	2.9b	(log.f64 (/.f64 (+.f64 N 1) N))
	0.0b	(/.f64 (+.f64 N 1) N)
✓	0.0b	(/.f64 (+.f64 N 1) N)
✓	2.9b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 17 to 11 computations (35.3% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite60.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

680×	`pow1_binary64`
635×	`log1p-expm1-u_binary64`
635×	`expm1-log1p-u_binary64`
634×	`add-log-exp_binary64`
622×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	127	15
2	1707	15

Stop Event

1×	node limit

Counts

2 → 60

Calls

Call 1

Inputs
(log.f64 (/.f64 (+.f64 N 1) N))
(/.f64 (+.f64 N 1) N)

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

Outputs

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

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

simplify48.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
701×	`associate-l_binary64`
458×	`fma-neg_binary64`
427×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	261
1	97	257
2	239	254
3	645	250
4	2107	250

Stop Event

1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

localize3.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (/.f64 1/2 N) N)
	0.0b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
✓	0.0b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
✓	0.1b	(/.f64 (/.f64 1/2 N) N)

Compiler

Compiled 24 to 16 computations (33.3% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(/.f64 (/.f64 1/2 N) N)
0.0ms	N	@	0	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
0.0ms	N	@	inf	(/.f64 (/.f64 1/2 N) N)
0.0ms	N	@	-inf	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
0.0ms	N	@	inf	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))

rewrite131.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

819×	`prod-diff_binary64`
434×	`log-prod_binary64`
301×	`fma-def_binary64`
285×	`pow-prod-down_binary64`
248×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	186	17
2	2794	17

Stop Event

1×	node limit

Counts

2 → 294

Calls

Call 1

Inputs
(/.f64 (/.f64 1/2 N) N)
(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))

Outputs

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simplify52.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

730×	`times-frac_binary64`
554×	`fma-neg_binary64`
534×	`associate-/r*_binary64`
494×	`associate-/l/_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	216
1	26	216
2	46	216
3	100	216
4	267	216
5	955	216
6	5068	216

Stop Event

1×	node limit

Counts

318 → 300

Calls

Call 1

Inputs
(/.f64 1/2 (pow.f64 N 2))
(/.f64 1/2 (pow.f64 N 2))
(/.f64 1/2 (pow.f64 N 2))
(/.f64 1/2 (pow.f64 N 2))
(/.f64 1/2 (pow.f64 N 2))
(/.f64 1/2 (pow.f64 N 2))
(/.f64 1/2 (pow.f64 N 2))
(/.f64 1/2 (pow.f64 N 2))
(/.f64 1/2 (pow.f64 N 2))
(/.f64 1/2 (pow.f64 N 2))
(/.f64 1/2 (pow.f64 N 2))
(/.f64 1/2 (pow.f64 N 2))
(/.f64 -1/2 (pow.f64 N 2))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))

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

localize21.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.4b	(/.f64 1 (*.f64 N N))
	0.4b	(/.f64 1/3 N)
	0.1b	(.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2))
	0.0b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
✓	0.0b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
✓	0.1b	(.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2))
✓	0.4b	(/.f64 1/3 N)
✓	0.4b	(/.f64 1 (*.f64 N N))

Compiler

Compiled 50 to 32 computations (36% saved)

series7.0ms (0.1%)

Counts

4 → 36

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	N	@	inf	(/.f64 1/3 N)
1.0ms	N	@	0	(.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2))
1.0ms	N	@	-inf	(.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2))
0.0ms	N	@	0	(/.f64 1 (*.f64 N N))
0.0ms	N	@	0	(/.f64 1/3 N)

rewrite94.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

564×	`log-prod_binary64`
422×	`fma-def_binary64`
322×	`pow2_binary64`
278×	`fma-neg_binary64`
221×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	274	38
2	3774	38

Stop Event

1×	node limit

Counts

4 → 193

Calls

Call 1

Inputs
(/.f64 1 (*.f64 N N))
(/.f64 1/3 N)
(.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2))
(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 N -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 N -2))) 2)) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 N -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (pow.f64 N -2)))) (log.f64 (sqrt.f64 (exp.f64 (pow.f64 N -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (pow.f64 N -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 N -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N -1) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 N -2)) (cbrt.f64 (/.f64 (pow.f64 N -3) N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 N -2)) (/.f64 (pow.f64 N -1) (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 N -2)) (.f64 (cbrt.f64 (pow.f64 N -1)) (pow.f64 N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (pow.f64 N -3) N)) (cbrt.f64 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N -1/2) (/.f64 (pow.f64 N -1) (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N -1/2) (.f64 (pow.f64 N -1/2) (pow.f64 N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (.f64 N (neg.f64 N))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 N -1/2) 3) (pow.f64 N -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (pow.f64 N 4))) (cbrt.f64 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 N -2)) 1) (/.f64 (cbrt.f64 (pow.f64 N -1)) N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 N -1/2) 1) (/.f64 (pow.f64 N -1/2) N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 N -2)) (pow.f64 (cbrt.f64 N) 2)) (cbrt.f64 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 N -1/2) (pow.f64 (cbrt.f64 N) 2)) (/.f64 (pow.f64 N -1/2) (cbrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (cbrt.f64 (pow.f64 N -2)) (sqrt.f64 N)) (/.f64 (cbrt.f64 (pow.f64 N -1)) (sqrt.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 N -1) (cbrt.f64 (pow.f64 N -2))) (cbrt.f64 (pow.f64 N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 N -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 N N) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 N -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 N -1) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 N -3) N) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (pow.f64 N -3) 2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 N -2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (neg.f64 N) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 N -3) (pow.f64 N 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (.f64 N (neg.f64 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 N -3) N))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 N -3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 N -3) (pow.f64 N 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -2 (log.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 2 (log.f64 N)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (*.f64 -2 (log.f64 N)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1/3 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1/3 N))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1/3 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/3 N)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1/3 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/3 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1/3 N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/3 (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/3 N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 N -1) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/3 N)) (pow.f64 (cbrt.f64 (/.f64 1/3 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 1/3 N)) 2) (cbrt.f64 (/.f64 1/3 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 1/3 N)) (sqrt.f64 (/.f64 1/3 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/3 (/.f64 1 (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/3 (cbrt.f64 (pow.f64 N -2))) (cbrt.f64 (pow.f64 N -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 1/3 (pow.f64 N -1/2)) (pow.f64 N -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/3 N) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/9 (pow.f64 N -2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/3 N)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/3 N)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/27 (pow.f64 N -3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 N 3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (.f64 N 3) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 1/9 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/3 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/3 N))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 1/27 (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/3 N)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/3 N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/3 N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 1/3 N)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (pow.f64 N -2) (+.f64 (/.f64 1/3 N) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 1/3 N) (pow.f64 N -2)) (.f64 -1/2 (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 N -2) (/.f64 1/3 N)) (.f64 (pow.f64 N -2) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 N -2))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 N -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 N -2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 N -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 N -2) (+.f64 (/.f64 1/3 N) -1/2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (/.f64 1/3 N) (.f64 N N)) (/.f64 1/2 (.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 N N) (+.f64 (/.f64 1/3 N) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 1/3 N) -1/2) (.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 1/3 N) -1/2) 2)) (/.f64 (.f64 N N) (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (/.f64 (.f64 N N) (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/27 (pow.f64 N -3) -1/8) (.f64 (.f64 N N) (+.f64 (fma.f64 1/9 (pow.f64 N -2) 1/4) (/.f64 1/6 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/9 (pow.f64 N -2) -1/4) (.f64 (.f64 N N) (+.f64 (/.f64 1/3 N) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (/.f64 1/3 N) -1/2)) (.f64 N (neg.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (+.f64 (/.f64 1/3 N) -1/2)) (.f64 N (neg.f64 N)))))) 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fma.f64 -1 (/.f64 1 (neg.f64 N)) (.f64 (pow.f64 N -2) (+.f64 (/.f64 1/3 N) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (cbrt.f64 (/.f64 (pow.f64 N -3) N))) (sqrt.f64 (cbrt.f64 (pow.f64 N -2))) (.f64 (pow.f64 N -2) (+.f64 (/.f64 1/3 N) -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (cbrt.f64 (pow.f64 N 4))) (/.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 (cbrt.f64 N) 2)) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 1/3 N) -1/2) 2)) 1) (/.f64 (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (.f64 N N)) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) 1) (/.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (.f64 N N)) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 1/3 N) -1/2) 2)) N) (/.f64 (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) N) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (cbrt.f64 (pow.f64 (+.f64 (/.f64 1/3 N) -1/2) 2)) (cbrt.f64 (pow.f64 N 4))) (cbrt.f64 (.f64 (pow.f64 N -2) (+.f64 (/.f64 1/3 N) -1/2))) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (cbrt.f64 (pow.f64 N 4))) (/.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 (cbrt.f64 N) 2)) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -1)) (pow.f64 N -1) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 N -2) (cbrt.f64 (pow.f64 (+.f64 (/.f64 1/3 N) -1/2) 2))) (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 N -2) (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2))) (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (cbrt.f64 (/.f64 (pow.f64 N -3) N))) (cbrt.f64 (pow.f64 N -2)) (pow.f64 N -1))))))

simplify66.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-neg_binary64`
688×	`distribute-neg-frac_binary64`
536×	`unswap-sqr_binary64`
478×	`associate-/r/_binary64`
332×	`associate-/r*_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	23	438
1	56	438
2	105	438
3	223	438
4	610	438
5	2588	426
6	6165	426

Stop Event

1×	node limit

Counts

229 → 206

Calls

Call 1

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

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

localize5.0ms (0.1%)

Compiler: Compiled 7 to 3 computations (57.1% saved)

eval726.0ms (8.7%)

Compiler: Compiled 13267 to 9727 computations (26.7% saved)

prune190.0ms (2.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	576	7	583
Fresh	2	0	2
Picked	0	1	1
Done	2	2	4
Total	580	10	590

Error

0.0b

Counts

590 → 10

Alt Table

Click to see full alt table

Status	Error	Program
▶	27.9b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N))))
	29.0b	(-.f64 N (log.f64 N))
▶	45.9b	(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))
✓	27.7b	(log.f64 (/.f64 (+.f64 N 1) N))
▶	34.2b	(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
✓	32.7b	(/.f64 1 N)
	53.2b	(/.f64 (-.f64 (.f64 N (.f64 N 2)) N) (.f64 N (.f64 N (*.f64 N 2))))
✓	29.9b	(neg.f64 (log.f64 N))
▶	33.7b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
▶	34.2b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)

Compiler

Compiled 181 to 127 computations (29.8% saved)

localize208.0ms (2.5%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.3b	(pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)
	0.3b	(cbrt.f64 (/.f64 (+.f64 N 1) N))
	0.2b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N))))
	0.0b	(/.f64 (+.f64 N 1) N)
✓	0.3b	(cbrt.f64 (/.f64 (+.f64 N 1) N))
✓	0.3b	(pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)
✓	2.6b	(log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2))
✓	2.7b	(log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)))

Compiler

Compiled 59 to 43 computations (27.1% saved)

series23.0ms (0.3%)

Counts

4 → 32

Calls

12 calls:

Time	Variable		Point	Expression
7.0ms	N	@	-inf	(log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)))
5.0ms	N	@	-inf	(log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2))
2.0ms	N	@	0	(log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2))
2.0ms	N	@	0	(log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)))
1.0ms	N	@	-inf	(pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)

rewrite135.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

937×	`pow1_binary64`
874×	`add-log-exp_binary64`
874×	`log1p-expm1-u_binary64`
874×	`expm1-log1p-u_binary64`
98×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	46
1	207	46
2	2495	46

Stop Event

1×	node limit

Counts

4 → 97

Calls

Call 1

Inputs
(log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)))
(log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2))
(pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)
(cbrt.f64 (/.f64 (+.f64 N 1) N))

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

simplify136.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-def_binary64`
413×	`associate-l_binary64`
374×	`associate-r_binary64`
363×	`distribute-rgt-in_binary64`
328×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	175	1083
1	533	953
2	1659	870
3	6222	850

Stop Event

1×	node limit

Counts

129 → 155

Calls

Call 1

Inputs
(/.f64 1/3 N)
(-.f64 (.f64 1/3 (/.f64 1 N)) (.f64 1/6 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 N 3))) (.f64 1/3 (/.f64 1 N))) (*.f64 1/6 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 N 3))) (.f64 1/3 (/.f64 1 N))) (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 2))) (.f64 1/12 (/.f64 1 (pow.f64 N 4)))))
(log.f64 (pow.f64 (cbrt.f64 -1) 2))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 2)) (.f64 -1/3 (.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 2)) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3)) (.f64 -1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3))) (pow.f64 N 2))) (.f64 -1/3 (*.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3)))))
(+.f64 (.f64 -1/6 (/.f64 (+.f64 (.f64 2/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (+.f64 (.f64 2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))) (.f64 2 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))))))) (pow.f64 N 3))) (+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 2)) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3)) (.f64 -1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3))) (pow.f64 N 2))) (.f64 -1/3 (*.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))))))
(/.f64 2/3 N)
(-.f64 (.f64 2/3 (/.f64 1 N)) (.f64 1/3 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 2/9 (/.f64 1 (pow.f64 N 3))) (.f64 2/3 (/.f64 1 N))) (*.f64 1/3 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 2/9 (/.f64 1 (pow.f64 N 3))) (.f64 2/3 (/.f64 1 N))) (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 4))) (.f64 1/3 (/.f64 1 (pow.f64 N 2)))))
(log.f64 (pow.f64 (cbrt.f64 -1) 4))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 4)) (.f64 -2/3 (.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 4)) (+.f64 (.f64 -2/3 (.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))) (.f64 1/2 (/.f64 (+.f64 (.f64 -4/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3)) (.f64 2 (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3)) (.f64 1/9 (pow.f64 (*.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3))) (pow.f64 (cbrt.f64 -1) 4)))) (pow.f64 N 2)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 4)) (+.f64 (.f64 -1/6 (/.f64 (+.f64 (.f64 6 (/.f64 (+.f64 (.f64 -2/3 (.f64 (cbrt.f64 -1) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))))) (.f64 -2/27 (.f64 (pow.f64 1 1/3) (/.f64 1 (cbrt.f64 -1))))) (pow.f64 (cbrt.f64 -1) 4))) (+.f64 (.f64 16/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (.f64 -4 (.f64 (+.f64 (.f64 -2/9 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3)) (.f64 1/9 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3))) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 17)) 1/3))))) (pow.f64 N 3))) (+.f64 (.f64 -2/3 (.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))) (.f64 1/2 (/.f64 (+.f64 (.f64 -4/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3)) (.f64 2 (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3)) (.f64 1/9 (pow.f64 (*.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3))) (pow.f64 (cbrt.f64 -1) 4)))) (pow.f64 N 2))))))
1
(+.f64 1 (*.f64 2/3 (/.f64 1 N)))
(-.f64 (+.f64 1 (.f64 2/3 (/.f64 1 N))) (.f64 1/9 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 1 (+.f64 (.f64 4/81 (/.f64 1 (pow.f64 N 3))) (.f64 2/3 (/.f64 1 N)))) (*.f64 1/9 (/.f64 1 (pow.f64 N 2))))
(pow.f64 (cbrt.f64 -1) 4)
(+.f64 (.f64 -2/3 (.f64 (/.f64 1 N) (pow.f64 (*.f64 1 (pow.f64 (cbrt.f64 -1) 7)) 1/3))) (pow.f64 (cbrt.f64 -1) 4))
(+.f64 (.f64 -2/3 (.f64 (/.f64 1 N) (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 7)) 1/3))) (+.f64 (.f64 -2/9 (.f64 (/.f64 1 (pow.f64 N 2)) (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3))) (+.f64 (pow.f64 (cbrt.f64 -1) 4) (.f64 1/9 (.f64 (/.f64 1 (pow.f64 N 2)) (pow.f64 (*.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3))))))
(+.f64 (.f64 -2/3 (.f64 (/.f64 1 N) (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 7)) 1/3))) (+.f64 (.f64 -2/9 (.f64 (/.f64 1 (pow.f64 N 2)) (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3))) (+.f64 (pow.f64 (cbrt.f64 -1) 4) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -2/3 (.f64 (cbrt.f64 -1) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))))) (.f64 -2/27 (.f64 (pow.f64 1 1/3) (/.f64 1 (cbrt.f64 -1))))) (pow.f64 N 3))) (.f64 1/9 (.f64 (/.f64 1 (pow.f64 N 2)) (pow.f64 (*.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3)))))))
1
(+.f64 1 (*.f64 1/3 (/.f64 1 N)))
(-.f64 (+.f64 1 (.f64 1/3 (/.f64 1 N))) (.f64 1/9 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 1 (+.f64 (.f64 5/81 (/.f64 1 (pow.f64 N 3))) (.f64 1/3 (/.f64 1 N)))) (*.f64 1/9 (/.f64 1 (pow.f64 N 2))))
(pow.f64 (cbrt.f64 -1) 2)
(+.f64 (pow.f64 (cbrt.f64 -1) 2) (.f64 -1/3 (.f64 (/.f64 1 N) (pow.f64 (*.f64 1 (cbrt.f64 -1)) 1/3))))
(+.f64 (.f64 -1/9 (.f64 (/.f64 1 (pow.f64 N 2)) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)) 1/3))) (+.f64 (pow.f64 (cbrt.f64 -1) 2) (.f64 -1/3 (.f64 (/.f64 1 N) (pow.f64 (*.f64 1 (cbrt.f64 -1)) 1/3)))))
(+.f64 (.f64 1/3 (/.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))) (.f64 (pow.f64 N 3) (cbrt.f64 -1)))) (+.f64 (.f64 -1/9 (.f64 (/.f64 1 (pow.f64 N 2)) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)) 1/3))) (+.f64 (pow.f64 (cbrt.f64 -1) 2) (.f64 -1/3 (.f64 (/.f64 1 N) (pow.f64 (.f64 1 (cbrt.f64 -1)) 1/3))))))

Outputs
(/.f64 1/3 N)
(-.f64 (.f64 1/3 (/.f64 1 N)) (.f64 1/6 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1/3 N) (/.f64 1/6 (*.f64 N N)))
(+.f64 (/.f64 1/3 N) (/.f64 -1/6 (*.f64 N N)))
(-.f64 (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 N 3))) (.f64 1/3 (/.f64 1 N))) (*.f64 1/6 (/.f64 1 (pow.f64 N 2))))
(+.f64 (/.f64 1/9 (pow.f64 N 3)) (-.f64 (/.f64 1/3 N) (/.f64 1/6 (*.f64 N N))))
(+.f64 (/.f64 1/3 N) (-.f64 (/.f64 1/9 (pow.f64 N 3)) (/.f64 1/6 (*.f64 N N))))
(+.f64 (/.f64 1/3 N) (+.f64 (/.f64 1/9 (pow.f64 N 3)) (/.f64 -1/6 (*.f64 N N))))
(-.f64 (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 N 3))) (.f64 1/3 (/.f64 1 N))) (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 2))) (.f64 1/12 (/.f64 1 (pow.f64 N 4)))))
(+.f64 (/.f64 1/9 (pow.f64 N 3)) (-.f64 (/.f64 1/3 N) (+.f64 (/.f64 1/6 (*.f64 N N)) (/.f64 1/12 (pow.f64 N 4)))))
(+.f64 (+.f64 (/.f64 1/3 N) (/.f64 1/9 (pow.f64 N 3))) (-.f64 (/.f64 -1/6 (*.f64 N N)) (/.f64 1/12 (pow.f64 N 4))))
(+.f64 (/.f64 1/3 N) (-.f64 (+.f64 (/.f64 1/9 (pow.f64 N 3)) (/.f64 -1/6 (*.f64 N N))) (/.f64 1/12 (pow.f64 N 4))))
(log.f64 (pow.f64 (cbrt.f64 -1) 2))
(*.f64 2 (log.f64 (cbrt.f64 -1)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 2)) (.f64 -1/3 (.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 2)) (.f64 -1/3 (.f64 (/.f64 1 N) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))))))
(fma.f64 2 (log.f64 (cbrt.f64 -1)) (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 -1/3 N)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 2)) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3)) (.f64 -1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3))) (pow.f64 N 2))) (.f64 -1/3 (*.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 2)) (fma.f64 1/2 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) -1/3) (.f64 N N)) (.f64 -1/3 (.f64 (/.f64 1 N) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))))))
(fma.f64 2 (log.f64 (cbrt.f64 -1)) (fma.f64 1/2 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) (/.f64 (.f64 N N) -1/3)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 -1/3 N))))
(fma.f64 -1/3 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) N) (fma.f64 2 (log.f64 (cbrt.f64 -1)) (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) -1/6) (.f64 N N))))
(fma.f64 2 (log.f64 (cbrt.f64 -1)) (.f64 (/.f64 -1/3 N) (+.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 (.f64 1/2 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)))) N))))
(+.f64 (.f64 -1/6 (/.f64 (+.f64 (.f64 2/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (+.f64 (.f64 2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))) (.f64 2 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))))))) (pow.f64 N 3))) (+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 2)) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3)) (.f64 -1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3))) (pow.f64 N 2))) (.f64 -1/3 (*.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))))))
(fma.f64 -1/6 (/.f64 (+.f64 (/.f64 2/27 (pow.f64 (cbrt.f64 -1) 5)) (fma.f64 2/9 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) (.f64 2 (+.f64 (/.f64 1/27 (pow.f64 (cbrt.f64 -1) 2)) (.f64 -2/9 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))))) (pow.f64 N 3)) (+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 2)) (fma.f64 1/2 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) -1/3) (.f64 N N)) (.f64 -1/3 (.f64 (/.f64 1 N) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))))))))
(fma.f64 -1/6 (/.f64 (+.f64 (.f64 2 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) -5/27)) (.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 8/27)) (pow.f64 N 3)) (fma.f64 2 (log.f64 (cbrt.f64 -1)) (fma.f64 1/2 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) (/.f64 (.f64 N N) -1/3)) (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 -1/3 N)))))
(fma.f64 -1/6 (/.f64 (fma.f64 2 (/.f64 -5/27 (pow.f64 (cbrt.f64 -1) 2)) (/.f64 8/27 (pow.f64 (cbrt.f64 -1) 5))) (pow.f64 N 3)) (fma.f64 -1/3 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) N) (fma.f64 2 (log.f64 (cbrt.f64 -1)) (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) -1/6) (.f64 N N)))))
(fma.f64 2 (log.f64 (cbrt.f64 -1)) (fma.f64 -1/6 (/.f64 (fma.f64 2 (/.f64 -5/27 (pow.f64 (cbrt.f64 -1) 2)) (/.f64 8/27 (pow.f64 (cbrt.f64 -1) 5))) (pow.f64 N 3)) (.f64 (/.f64 -1/3 N) (+.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 (.f64 1/2 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)))) N)))))
(/.f64 2/3 N)
(-.f64 (.f64 2/3 (/.f64 1 N)) (.f64 1/3 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 2/3 N) (/.f64 1/3 (*.f64 N N)))
(+.f64 (/.f64 2/3 N) (/.f64 -1/3 (*.f64 N N)))
(-.f64 (+.f64 (.f64 2/9 (/.f64 1 (pow.f64 N 3))) (.f64 2/3 (/.f64 1 N))) (*.f64 1/3 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (/.f64 2/3 N) (/.f64 2/9 (pow.f64 N 3))) (/.f64 1/3 (*.f64 N N)))
(+.f64 (/.f64 2/3 N) (+.f64 (/.f64 2/9 (pow.f64 N 3)) (/.f64 -1/3 (*.f64 N N))))
(+.f64 (+.f64 (/.f64 2/3 N) (/.f64 2/9 (pow.f64 N 3))) (/.f64 -1/3 (*.f64 N N)))
(-.f64 (+.f64 (.f64 2/9 (/.f64 1 (pow.f64 N 3))) (.f64 2/3 (/.f64 1 N))) (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 4))) (.f64 1/3 (/.f64 1 (pow.f64 N 2)))))
(-.f64 (+.f64 (/.f64 2/3 N) (/.f64 2/9 (pow.f64 N 3))) (+.f64 (/.f64 1/3 (*.f64 N N)) (/.f64 1/6 (pow.f64 N 4))))
(+.f64 (/.f64 2/3 N) (-.f64 (/.f64 2/9 (pow.f64 N 3)) (+.f64 (/.f64 1/3 (*.f64 N N)) (/.f64 1/6 (pow.f64 N 4)))))
(+.f64 (/.f64 -1/3 (*.f64 N N)) (+.f64 (+.f64 (/.f64 2/3 N) (/.f64 2/9 (pow.f64 N 3))) (/.f64 -1/6 (pow.f64 N 4))))
(+.f64 (/.f64 2/3 N) (+.f64 (/.f64 2/9 (pow.f64 N 3)) (+.f64 (/.f64 -1/3 (*.f64 N N)) (/.f64 -1/6 (pow.f64 N 4)))))
(log.f64 (pow.f64 (cbrt.f64 -1) 4))
(*.f64 4 (log.f64 (cbrt.f64 -1)))
(log.f64 (neg.f64 (cbrt.f64 -1)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 4)) (.f64 -2/3 (.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 4)) (.f64 (.f64 (/.f64 1 N) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))) -2/3))
(fma.f64 (/.f64 -2/3 N) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (*.f64 4 (log.f64 (cbrt.f64 -1))))
(fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 -2/3 N) (*.f64 4 (log.f64 (cbrt.f64 -1))))
(fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 -2/3 N) (log.f64 (neg.f64 (cbrt.f64 -1))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 4)) (+.f64 (.f64 -2/3 (.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))) (.f64 1/2 (/.f64 (+.f64 (.f64 -4/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3)) (.f64 2 (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3)) (.f64 1/9 (pow.f64 (*.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3))) (pow.f64 (cbrt.f64 -1) 4)))) (pow.f64 N 2)))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 4)) (fma.f64 -2/3 (.f64 (/.f64 1 N) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))) (.f64 1/2 (/.f64 (fma.f64 -4/9 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) (.f64 2 (/.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) -1/9) (pow.f64 (cbrt.f64 -1) 4)))) (*.f64 N N)))))
(fma.f64 4 (log.f64 (cbrt.f64 -1)) (fma.f64 1/2 (/.f64 (fma.f64 2 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) (/.f64 (pow.f64 (cbrt.f64 -1) 4) -1/9)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) -4/9)) (.f64 N N)) (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 -2/3 N))))
(fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 -2/3 N) (fma.f64 4 (log.f64 (cbrt.f64 -1)) (/.f64 (+.f64 (.f64 -2/9 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)))) (.f64 1/9 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) (cbrt.f64 -1)))) (*.f64 N N))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 4)) (+.f64 (.f64 -1/6 (/.f64 (+.f64 (.f64 6 (/.f64 (+.f64 (.f64 -2/3 (.f64 (cbrt.f64 -1) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))))) (.f64 -2/27 (.f64 (pow.f64 1 1/3) (/.f64 1 (cbrt.f64 -1))))) (pow.f64 (cbrt.f64 -1) 4))) (+.f64 (.f64 16/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (.f64 -4 (.f64 (+.f64 (.f64 -2/9 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3)) (.f64 1/9 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3))) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 17)) 1/3))))) (pow.f64 N 3))) (+.f64 (.f64 -2/3 (.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))) (.f64 1/2 (/.f64 (+.f64 (.f64 -4/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3)) (.f64 2 (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3)) (.f64 1/9 (pow.f64 (*.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3))) (pow.f64 (cbrt.f64 -1) 4)))) (pow.f64 N 2))))))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 -1) 4)) (fma.f64 -1/6 (/.f64 (fma.f64 6 (/.f64 (fma.f64 -2/3 (.f64 (cbrt.f64 -1) (+.f64 (/.f64 1/27 (pow.f64 (cbrt.f64 -1) 2)) (.f64 -2/9 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))) (.f64 -2/27 (/.f64 1 (cbrt.f64 -1)))) (pow.f64 (cbrt.f64 -1) 4)) (+.f64 (/.f64 16/27 (pow.f64 (cbrt.f64 -1) 5)) (.f64 -4 (.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) -1/9) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 17))))))) (pow.f64 N 3)) (fma.f64 -2/3 (.f64 (/.f64 1 N) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))) (.f64 1/2 (/.f64 (fma.f64 -4/9 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) (.f64 2 (/.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) -1/9) (pow.f64 (cbrt.f64 -1) 4)))) (*.f64 N N))))))
(fma.f64 4 (log.f64 (cbrt.f64 -1)) (fma.f64 -1/6 (/.f64 (fma.f64 6 (/.f64 (fma.f64 (.f64 (cbrt.f64 -1) -2/3) (.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) -5/27) (/.f64 -2/27 (cbrt.f64 -1))) (pow.f64 (cbrt.f64 -1) 4)) (fma.f64 -4 (.f64 (.f64 -1/9 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2))) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 17)))) (/.f64 16/27 (pow.f64 (cbrt.f64 -1) 5)))) (pow.f64 N 3)) (fma.f64 1/2 (/.f64 (fma.f64 2 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) (/.f64 (pow.f64 (cbrt.f64 -1) 4) -1/9)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) -4/9)) (.f64 N N)) (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 -2/3 N)))))
(fma.f64 4 (log.f64 (cbrt.f64 -1)) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 -2/3 N) (fma.f64 -1/6 (/.f64 (+.f64 (/.f64 16/27 (pow.f64 (cbrt.f64 -1) 5)) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 17))) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) 4/9) (.f64 (/.f64 (fma.f64 (cbrt.f64 -1) (.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 10/81) (/.f64 -2/27 (cbrt.f64 -1))) (cbrt.f64 -1)) -6))) (pow.f64 N 3)) (/.f64 (+.f64 (.f64 -2/9 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)))) (.f64 1/9 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) (cbrt.f64 -1)))) (.f64 N N)))))
(fma.f64 4 (log.f64 (cbrt.f64 -1)) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 -2/3 N) (fma.f64 -1/6 (/.f64 (+.f64 (/.f64 16/27 (pow.f64 (cbrt.f64 -1) 5)) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 17))) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) 4/9) (.f64 (/.f64 (+.f64 (.f64 (/.f64 1 (cbrt.f64 -1)) 10/81) (/.f64 -2/27 (cbrt.f64 -1))) (cbrt.f64 -1)) -6))) (pow.f64 N 3)) (/.f64 (+.f64 (.f64 -2/9 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)))) (.f64 1/9 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) (cbrt.f64 -1)))) (.f64 N N)))))
1
(+.f64 1 (*.f64 2/3 (/.f64 1 N)))
(+.f64 1 (/.f64 2/3 N))
(-.f64 (+.f64 1 (.f64 2/3 (/.f64 1 N))) (.f64 1/9 (/.f64 1 (pow.f64 N 2))))
(+.f64 1 (-.f64 (/.f64 2/3 N) (/.f64 1/9 (*.f64 N N))))
(+.f64 (+.f64 1 (/.f64 2/3 N)) (/.f64 -1/9 (*.f64 N N)))
(+.f64 1 (+.f64 (/.f64 2/3 N) (/.f64 -1/9 (*.f64 N N))))
(-.f64 (+.f64 1 (+.f64 (.f64 4/81 (/.f64 1 (pow.f64 N 3))) (.f64 2/3 (/.f64 1 N)))) (*.f64 1/9 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 1 (+.f64 (/.f64 2/3 N) (/.f64 4/81 (pow.f64 N 3)))) (/.f64 1/9 (*.f64 N N)))
(+.f64 1 (+.f64 (/.f64 4/81 (pow.f64 N 3)) (+.f64 (/.f64 2/3 N) (/.f64 -1/9 (*.f64 N N)))))
(+.f64 1 (+.f64 (/.f64 2/3 N) (+.f64 (/.f64 4/81 (pow.f64 N 3)) (/.f64 -1/9 (*.f64 N N)))))
(+.f64 (/.f64 2/3 N) (+.f64 (/.f64 4/81 (pow.f64 N 3)) (+.f64 1 (/.f64 -1/9 (*.f64 N N)))))
(pow.f64 (cbrt.f64 -1) 4)
(*.f64 -1 (cbrt.f64 -1))
(neg.f64 (cbrt.f64 -1))
(+.f64 (.f64 -2/3 (.f64 (/.f64 1 N) (pow.f64 (*.f64 1 (pow.f64 (cbrt.f64 -1) 7)) 1/3))) (pow.f64 (cbrt.f64 -1) 4))
(fma.f64 -2/3 (*.f64 (/.f64 1 N) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 7))) (pow.f64 (cbrt.f64 -1) 4))
(fma.f64 -2/3 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 7)) N) (pow.f64 (cbrt.f64 -1) 4))
(fma.f64 -1 (cbrt.f64 -1) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 7)) (/.f64 -2/3 N)))
(fma.f64 -2/3 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 7)) N) (neg.f64 (cbrt.f64 -1)))
(+.f64 (.f64 -2/3 (.f64 (/.f64 1 N) (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 7)) 1/3))) (+.f64 (.f64 -2/9 (.f64 (/.f64 1 (pow.f64 N 2)) (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3))) (+.f64 (pow.f64 (cbrt.f64 -1) 4) (.f64 1/9 (.f64 (/.f64 1 (pow.f64 N 2)) (pow.f64 (*.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3))))))
(fma.f64 -2/3 (.f64 (/.f64 1 N) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 7))) (fma.f64 -2/9 (.f64 (/.f64 1 (.f64 N N)) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2))) (+.f64 (pow.f64 (cbrt.f64 -1) 4) (.f64 (/.f64 1/9 (*.f64 N N)) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2))))))
(fma.f64 -2/3 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 7)) N) (fma.f64 -2/9 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) (.f64 N N)) (fma.f64 (/.f64 1/9 (.f64 N N)) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) (pow.f64 (cbrt.f64 -1) 4))))
(fma.f64 -2/3 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 7)) N) (fma.f64 -1 (cbrt.f64 -1) (.f64 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) (.f64 N N)) -1/9)))
(fma.f64 -2/3 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 7)) N) (fma.f64 -1 (cbrt.f64 -1) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) (/.f64 -1/9 (.f64 N N)))))
(+.f64 (.f64 -2/3 (.f64 (/.f64 1 N) (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 7)) 1/3))) (+.f64 (.f64 -2/9 (.f64 (/.f64 1 (pow.f64 N 2)) (pow.f64 (.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3))) (+.f64 (pow.f64 (cbrt.f64 -1) 4) (+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 -2/3 (.f64 (cbrt.f64 -1) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))))) (.f64 -2/27 (.f64 (pow.f64 1 1/3) (/.f64 1 (cbrt.f64 -1))))) (pow.f64 N 3))) (.f64 1/9 (.f64 (/.f64 1 (pow.f64 N 2)) (pow.f64 (*.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 1/3)))))))
(fma.f64 -2/3 (.f64 (/.f64 1 N) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 7))) (fma.f64 -2/9 (.f64 (/.f64 1 (.f64 N N)) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2))) (+.f64 (pow.f64 (cbrt.f64 -1) 4) (fma.f64 -1 (/.f64 (fma.f64 -2/3 (.f64 (cbrt.f64 -1) (+.f64 (/.f64 1/27 (pow.f64 (cbrt.f64 -1) 2)) (.f64 -2/9 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))) (.f64 -2/27 (/.f64 1 (cbrt.f64 -1)))) (pow.f64 N 3)) (.f64 (/.f64 1/9 (.f64 N N)) (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)))))))
(fma.f64 -2/3 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 7)) N) (+.f64 (-.f64 (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) (/.f64 1/9 (.f64 N N))) (/.f64 (fma.f64 (.f64 (cbrt.f64 -1) -2/3) (.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) -5/27) (/.f64 -2/27 (cbrt.f64 -1))) (pow.f64 N 3))) (fma.f64 -2/9 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) (*.f64 N N)) (pow.f64 (cbrt.f64 -1) 4))))
(-.f64 (fma.f64 -2/3 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 7)) N) (fma.f64 -1 (cbrt.f64 -1) (.f64 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) (.f64 N N)) -1/9))) (/.f64 (fma.f64 (cbrt.f64 -1) (*.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 10/81) (/.f64 -2/27 (cbrt.f64 -1))) (pow.f64 N 3)))
(fma.f64 -2/3 (/.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 7)) N) (fma.f64 -1 (cbrt.f64 -1) (fma.f64 (cbrt.f64 (pow.f64 (cbrt.f64 -1) 2)) (/.f64 -1/9 (.f64 N N)) (/.f64 (-.f64 (/.f64 2/27 (cbrt.f64 -1)) (.f64 (/.f64 1 (cbrt.f64 -1)) 10/81)) (pow.f64 N 3)))))
1
(+.f64 1 (*.f64 1/3 (/.f64 1 N)))
(+.f64 1 (/.f64 1/3 N))
(-.f64 (+.f64 1 (.f64 1/3 (/.f64 1 N))) (.f64 1/9 (/.f64 1 (pow.f64 N 2))))
(+.f64 1 (-.f64 (/.f64 1/3 N) (/.f64 1/9 (*.f64 N N))))
(+.f64 1 (+.f64 (/.f64 1/3 N) (/.f64 -1/9 (*.f64 N N))))
(-.f64 (+.f64 1 (+.f64 (.f64 5/81 (/.f64 1 (pow.f64 N 3))) (.f64 1/3 (/.f64 1 N)))) (*.f64 1/9 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 1 (+.f64 (/.f64 1/3 N) (/.f64 5/81 (pow.f64 N 3)))) (/.f64 1/9 (*.f64 N N)))
(+.f64 1 (+.f64 (/.f64 1/3 N) (-.f64 (/.f64 5/81 (pow.f64 N 3)) (/.f64 1/9 (*.f64 N N)))))
(+.f64 1 (+.f64 (/.f64 5/81 (pow.f64 N 3)) (+.f64 (/.f64 1/3 N) (/.f64 -1/9 (*.f64 N N)))))
(pow.f64 (cbrt.f64 -1) 2)
(+.f64 (pow.f64 (cbrt.f64 -1) 2) (.f64 -1/3 (.f64 (/.f64 1 N) (pow.f64 (*.f64 1 (cbrt.f64 -1)) 1/3))))
(+.f64 (pow.f64 (cbrt.f64 -1) 2) (.f64 -1/3 (.f64 (/.f64 1 N) (cbrt.f64 (cbrt.f64 -1)))))
(fma.f64 -1/3 (/.f64 (cbrt.f64 (cbrt.f64 -1)) N) (pow.f64 (cbrt.f64 -1) 2))
(+.f64 (.f64 -1/9 (.f64 (/.f64 1 (pow.f64 N 2)) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)) 1/3))) (+.f64 (pow.f64 (cbrt.f64 -1) 2) (.f64 -1/3 (.f64 (/.f64 1 N) (pow.f64 (*.f64 1 (cbrt.f64 -1)) 1/3)))))
(fma.f64 -1/9 (.f64 (/.f64 1 (.f64 N N)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)))) (+.f64 (pow.f64 (cbrt.f64 -1) 2) (.f64 -1/3 (.f64 (/.f64 1 N) (cbrt.f64 (cbrt.f64 -1))))))
(fma.f64 -1/9 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4))) (*.f64 N N)) (fma.f64 -1/3 (/.f64 (cbrt.f64 (cbrt.f64 -1)) N) (pow.f64 (cbrt.f64 -1) 2)))
(fma.f64 -1/3 (/.f64 (cbrt.f64 (cbrt.f64 -1)) N) (fma.f64 -1/9 (/.f64 (cbrt.f64 (/.f64 -1 (cbrt.f64 -1))) (*.f64 N N)) (pow.f64 (cbrt.f64 -1) 2)))
(+.f64 (.f64 1/3 (/.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))) (.f64 (pow.f64 N 3) (cbrt.f64 -1)))) (+.f64 (.f64 -1/9 (.f64 (/.f64 1 (pow.f64 N 2)) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)) 1/3))) (+.f64 (pow.f64 (cbrt.f64 -1) 2) (.f64 -1/3 (.f64 (/.f64 1 N) (pow.f64 (.f64 1 (cbrt.f64 -1)) 1/3))))))
(fma.f64 1/3 (/.f64 (+.f64 (/.f64 1/27 (pow.f64 (cbrt.f64 -1) 2)) (.f64 -2/9 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))) (.f64 (pow.f64 N 3) (cbrt.f64 -1))) (fma.f64 -1/9 (.f64 (/.f64 1 (.f64 N N)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4)))) (+.f64 (pow.f64 (cbrt.f64 -1) 2) (.f64 -1/3 (.f64 (/.f64 1 N) (cbrt.f64 (cbrt.f64 -1)))))))
(fma.f64 1/3 (/.f64 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) -5/27) (.f64 (pow.f64 N 3) (cbrt.f64 -1))) (fma.f64 -1/9 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 4))) (*.f64 N N)) (fma.f64 -1/3 (/.f64 (cbrt.f64 (cbrt.f64 -1)) N) (pow.f64 (cbrt.f64 -1) 2))))
(fma.f64 1/3 (/.f64 (/.f64 -5/27 (pow.f64 (cbrt.f64 -1) 2)) (.f64 (pow.f64 N 3) (cbrt.f64 -1))) (fma.f64 -1/3 (/.f64 (cbrt.f64 (cbrt.f64 -1)) N) (fma.f64 -1/9 (/.f64 (cbrt.f64 (/.f64 -1 (cbrt.f64 -1))) (.f64 N N)) (pow.f64 (cbrt.f64 -1) 2))))

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
	0.0b	(+.f64 1 (/.f64 -1/2 N))
✓	0.0b	(+.f64 1 (/.f64 -1/2 N))
✓	0.1b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)

Compiler

Compiled 19 to 14 computations (26.3% saved)

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
1.0ms	N	@	-inf	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
1.0ms	N	@	inf	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
0.0ms	N	@	0	(+.f64 1 (/.f64 -1/2 N))
0.0ms	N	@	inf	(+.f64 1 (/.f64 -1/2 N))

rewrite90.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

809×	`pow1_binary64`
760×	`add-log-exp_binary64`
759×	`log1p-expm1-u_binary64`
759×	`expm1-log1p-u_binary64`
747×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	154	17
2	2042	17

Stop Event

1×	node limit

Counts

2 → 62

Calls

Call 1

Inputs
(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
(+.f64 1 (/.f64 -1/2 N))

Outputs

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

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

simplify84.0ms (1%)

Algorithm

1×	egg-herbie

Rules

633×	`div-sub_binary64`
561×	`associate-/l*_binary64`
444×	`associate-/r/_binary64`
437×	`fma-neg_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	201
1	35	201
2	61	201
3	138	201
4	384	201
5	1509	201
6	4526	201
7	6960	201

Stop Event

1×	node limit

Counts

86 → 71

Calls

Call 1

Inputs
(/.f64 -1/2 (pow.f64 N 2))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(/.f64 -1/2 N)
(-.f64 1 (*.f64 1/2 (/.f64 1 N)))
(-.f64 1 (*.f64 1/2 (/.f64 1 N)))
(-.f64 1 (*.f64 1/2 (/.f64 1 N)))
1
(-.f64 1 (*.f64 1/2 (/.f64 1 N)))
(-.f64 1 (*.f64 1/2 (/.f64 1 N)))
(-.f64 1 (*.f64 1/2 (/.f64 1 N)))
1
(-.f64 1 (*.f64 1/2 (/.f64 1 N)))
(-.f64 1 (*.f64 1/2 (/.f64 1 N)))
(-.f64 1 (*.f64 1/2 (/.f64 1 N)))

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

localize27.0ms (0.3%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.1b	(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
	0.1b	(/.f64 N (+.f64 1 (/.f64 -1/2 N)))
	0.0b	(+.f64 1 (/.f64 -1/2 N))
	0.0b	(+.f64 1 (/.f64 -1/2 N))
✓	0.1b	(/.f64 N (+.f64 1 (/.f64 -1/2 N)))
✓	0.1b	(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))

Compiler

Compiled 28 to 21 computations (25% saved)

series4.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(/.f64 N (+.f64 1 (/.f64 -1/2 N)))
1.0ms	N	@	inf	(/.f64 N (+.f64 1 (/.f64 -1/2 N)))
1.0ms	N	@	0	(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
1.0ms	N	@	-inf	(/.f64 N (+.f64 1 (/.f64 -1/2 N)))
0.0ms	N	@	inf	(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))

rewrite75.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

937×	`pow1_binary64`
877×	`add-log-exp_binary64`
876×	`log1p-expm1-u_binary64`
876×	`expm1-log1p-u_binary64`
90×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	182	20
2	2461	20

Stop Event

1×	node limit

Counts

2 → 75

Calls

Call 1

Inputs
(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
(/.f64 N (+.f64 1 (/.f64 -1/2 N)))

Outputs

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

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

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Rules

887×	`fma-def_binary64`
648×	`times-frac_binary64`
509×	`associate-*l/_binary64`
482×	`fma-neg_binary64`
428×	`associate-*r/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	270
1	105	270
2	232	268
3	630	261
4	1676	255
5	4128	255
6	7725	255

Stop Event

1×	node limit

Counts

99 → 94

Calls

Call 1

Inputs
(/.f64 -1/2 (pow.f64 N 2))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(*.f64 -2 (pow.f64 N 2))
(+.f64 (.f64 -4 (pow.f64 N 3)) (.f64 -2 (pow.f64 N 2)))
(+.f64 (.f64 -4 (pow.f64 N 3)) (+.f64 (.f64 -2 (pow.f64 N 2)) (*.f64 -8 (pow.f64 N 4))))
(+.f64 (.f64 -4 (pow.f64 N 3)) (+.f64 (.f64 -2 (pow.f64 N 2)) (+.f64 (.f64 -16 (pow.f64 N 5)) (.f64 -8 (pow.f64 N 4)))))
N
(+.f64 N 1/2)
(+.f64 N (+.f64 1/2 (*.f64 1/4 (/.f64 1 N))))
(+.f64 N (+.f64 1/2 (+.f64 (.f64 1/4 (/.f64 1 N)) (.f64 1/8 (/.f64 1 (pow.f64 N 2))))))
N
(+.f64 N 1/2)
(+.f64 N (+.f64 1/2 (*.f64 1/4 (/.f64 1 N))))
(+.f64 N (+.f64 1/2 (+.f64 (.f64 1/4 (/.f64 1 N)) (.f64 1/8 (/.f64 1 (pow.f64 N 2))))))

Outputs
(/.f64 -1/2 (pow.f64 N 2))
(/.f64 -1/2 (*.f64 N N))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(*.f64 -2 (pow.f64 N 2))
(.f64 (.f64 N N) -2)
(.f64 N (.f64 N -2))
(+.f64 (.f64 -4 (pow.f64 N 3)) (.f64 -2 (pow.f64 N 2)))
(fma.f64 -4 (pow.f64 N 3) (.f64 (.f64 N N) -2))
(fma.f64 (.f64 N N) -2 (.f64 -4 (pow.f64 N 3)))
(.f64 (.f64 N N) (+.f64 -2 (*.f64 N -4)))
(.f64 (.f64 N N) (fma.f64 N -4 -2))
(+.f64 (.f64 -4 (pow.f64 N 3)) (+.f64 (.f64 -2 (pow.f64 N 2)) (*.f64 -8 (pow.f64 N 4))))
(fma.f64 -4 (pow.f64 N 3) (fma.f64 -2 (.f64 N N) (.f64 -8 (pow.f64 N 4))))
(fma.f64 -4 (pow.f64 N 3) (fma.f64 (.f64 N N) -2 (.f64 -8 (pow.f64 N 4))))
(fma.f64 -8 (pow.f64 N 4) (.f64 (.f64 N N) (+.f64 -2 (*.f64 N -4))))
(fma.f64 N (.f64 N (fma.f64 N -4 -2)) (.f64 -8 (pow.f64 N 4)))
(.f64 N (.f64 N (fma.f64 N (fma.f64 N -8 -4) -2)))
(+.f64 (.f64 -4 (pow.f64 N 3)) (+.f64 (.f64 -2 (pow.f64 N 2)) (+.f64 (.f64 -16 (pow.f64 N 5)) (.f64 -8 (pow.f64 N 4)))))
(fma.f64 -4 (pow.f64 N 3) (fma.f64 -2 (.f64 N N) (fma.f64 -16 (pow.f64 N 5) (.f64 -8 (pow.f64 N 4)))))
(fma.f64 -4 (pow.f64 N 3) (fma.f64 (.f64 N N) -2 (fma.f64 -8 (pow.f64 N 4) (.f64 -16 (pow.f64 N 5)))))
(fma.f64 N (.f64 N -2) (fma.f64 -4 (pow.f64 N 3) (fma.f64 -8 (pow.f64 N 4) (.f64 -16 (pow.f64 N 5)))))
(fma.f64 N (.f64 N (fma.f64 N -4 -2)) (fma.f64 -8 (pow.f64 N 4) (.f64 -16 (pow.f64 N 5))))
(fma.f64 N (.f64 N (fma.f64 N (fma.f64 N -8 -4) -2)) (.f64 -16 (pow.f64 N 5)))
N
(+.f64 N 1/2)
(+.f64 N (+.f64 1/2 (*.f64 1/4 (/.f64 1 N))))
(+.f64 N (+.f64 1/2 (/.f64 1/4 N)))
(+.f64 (+.f64 N 1/2) (/.f64 1/4 N))
(+.f64 N (+.f64 1/2 (+.f64 (.f64 1/4 (/.f64 1 N)) (.f64 1/8 (/.f64 1 (pow.f64 N 2))))))
(+.f64 N (+.f64 1/2 (+.f64 (/.f64 1/4 N) (/.f64 1/8 (*.f64 N N)))))
(+.f64 N (+.f64 (/.f64 1/4 N) (+.f64 1/2 (/.f64 1/8 (*.f64 N N)))))
(+.f64 N (+.f64 1/2 (+.f64 (/.f64 1/4 N) (/.f64 (/.f64 1/8 N) N))))
(+.f64 N (+.f64 (+.f64 1/2 (/.f64 1/4 N)) (/.f64 1/8 (*.f64 N N))))
N
(+.f64 N 1/2)
(+.f64 N (+.f64 1/2 (*.f64 1/4 (/.f64 1 N))))
(+.f64 N (+.f64 1/2 (/.f64 1/4 N)))
(+.f64 (+.f64 N 1/2) (/.f64 1/4 N))
(+.f64 N (+.f64 1/2 (+.f64 (.f64 1/4 (/.f64 1 N)) (.f64 1/8 (/.f64 1 (pow.f64 N 2))))))
(+.f64 N (+.f64 1/2 (+.f64 (/.f64 1/4 N) (/.f64 1/8 (*.f64 N N)))))
(+.f64 N (+.f64 (/.f64 1/4 N) (+.f64 1/2 (/.f64 1/8 (*.f64 N N)))))
(+.f64 N (+.f64 1/2 (+.f64 (/.f64 1/4 N) (/.f64 (/.f64 1/8 N) N))))
(+.f64 N (+.f64 (+.f64 1/2 (/.f64 1/4 N)) (/.f64 1/8 (*.f64 N N))))

localize19.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	11.8b	(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))
✓	11.8b	(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))

Compiler

Compiled 32 to 17 computations (46.9% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	N	@	0	(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))
0.0ms	N	@	-inf	(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))
0.0ms	N	@	inf	(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))

rewrite161.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

884×	`prod-diff_binary64`
544×	`log-prod_binary64`
280×	`fma-def_binary64`
259×	`pow2_binary64`
218×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	191	16
2	3060	16

Stop Event

1×	node limit

Counts

1 → 199

Calls

Call 1

Inputs
(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))

Outputs

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

simplify45.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

732×	`times-frac_binary64`
554×	`fma-neg_binary64`
536×	`associate-/r*_binary64`
494×	`associate-/l/_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	132
1	26	132
2	46	132
3	100	132
4	263	132
5	947	132
6	5090	132

Stop Event

1×	node limit

Counts

211 → 204

Calls

Call 1

Inputs
(/.f64 -1/2 (pow.f64 N 2))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))

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

localize35.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.4b	(/.f64 1/3 N)
	0.1b	(/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)
	0.1b	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
	0.0b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
✓	0.0b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
✓	0.1b	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
✓	0.1b	(/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)
	0.4b	(/.f64 1/3 N)

Compiler

Compiled 45 to 32 computations (28.9% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	N	@	-inf	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
0.0ms	N	@	0	(/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)
0.0ms	N	@	inf	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
0.0ms	N	@	0	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
0.0ms	N	@	inf	(/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)

rewrite104.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

601×	`log-prod_binary64`
407×	`fma-def_binary64`
326×	`pow2_binary64`
315×	`log-div_binary64`
262×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	258	42
2	3889	40

Stop Event

1×	node limit

Counts

3 → 180

Calls

Call 1

Inputs
(/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)
(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2))))) (log.f64 (sqrt.f64 (exp.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) (/.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x 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simplify66.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

617×	`fma-def_binary64`
536×	`unswap-sqr_binary64`
482×	`distribute-neg-frac_binary64`
401×	`div-sub_binary64`
356×	`*-commutative_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	28	486
1	69	486
2	127	486
3	274	486
4	802	486
5	3478	474
6	7161	474

Stop Event

1×	node limit

Counts

216 → 196

Calls

Call 1

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

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

eval810.0ms (9.7%)

Compiler: Compiled 22506 to 15973 computations (29% saved)

prune105.0ms (1.3%)

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	826	3	829
Fresh	0	2	2
Picked	0	1	1
Done	3	4	7
Total	829	10	839

Error

0.0b

Counts

839 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	27.9b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N))))
▶	29.0b	(-.f64 N (log.f64 N))
✓	32.7b	(/.f64 1 N)
▶	27.9b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 (cbrt.f64 N))))
▶	29.4b	(/.f64 1 (+.f64 N 1/2))
▶	53.2b	(/.f64 (-.f64 (.f64 N (.f64 N 2)) N) (.f64 N (.f64 N (*.f64 N 2))))
✓	29.9b	(neg.f64 (log.f64 N))
▶	27.9b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (log.f64 (/.f64 1 (cbrt.f64 (/.f64 N (+.f64 N 1))))))
✓	33.7b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
✓	27.7b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 181 to 135 computations (25.4% saved)

localize41.0ms (0.5%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.2b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (log.f64 (/.f64 1 (cbrt.f64 (/.f64 N (+.f64 N 1))))))
	0.1b	(/.f64 1 (cbrt.f64 (/.f64 N (+.f64 N 1))))
	0.0b	(/.f64 (+.f64 N 1) N)
	0.0b	(/.f64 N (+.f64 N 1))
	0.3b	(pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)
✓	0.4b	(cbrt.f64 (/.f64 N (+.f64 N 1)))
	2.6b	(log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2))
✓	2.7b	(log.f64 (/.f64 1 (cbrt.f64 (/.f64 N (+.f64 N 1)))))

Compiler

Compiled 82 to 60 computations (26.8% saved)

series8.0ms (0.1%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	N	@	-inf	(log.f64 (/.f64 1 (cbrt.f64 (/.f64 N (+.f64 N 1)))))
1.0ms	N	@	-inf	(cbrt.f64 (/.f64 N (+.f64 N 1)))
1.0ms	N	@	0	(cbrt.f64 (/.f64 N (+.f64 N 1)))
1.0ms	N	@	0	(log.f64 (/.f64 1 (cbrt.f64 (/.f64 N (+.f64 N 1)))))
0.0ms	N	@	inf	(log.f64 (/.f64 1 (cbrt.f64 (/.f64 N (+.f64 N 1)))))

rewrite105.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

868×	`pow1_binary64`
812×	`log1p-expm1-u_binary64`
812×	`expm1-log1p-u_binary64`
811×	`add-log-exp_binary64`
793×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	173	22
2	2275	22

Stop Event

1×	node limit

Counts

2 → 56

Calls

Call 1

Inputs
(log.f64 (/.f64 1 (cbrt.f64 (/.f64 N (+.f64 N 1)))))
(cbrt.f64 (/.f64 N (+.f64 N 1)))

Outputs

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

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

simplify90.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

585×	`distribute-rgt-in_binary64`
570×	`fma-def_binary64`
374×	`associate-l_binary64`
345×	`associate-r_binary64`
299×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	719
1	405	621
2	1325	558
3	5661	535

Stop Event

1×	node limit

Counts

72 → 85

Calls

Call 1

Inputs
(/.f64 1/3 N)
(-.f64 (.f64 1/3 (/.f64 1 N)) (.f64 1/6 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 N 3))) (.f64 1/3 (/.f64 1 N))) (*.f64 1/6 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 N 3))) (.f64 1/3 (/.f64 1 N))) (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 2))) (.f64 1/12 (/.f64 1 (pow.f64 N 4)))))
(.f64 -1/3 (.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3)))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3)) (.f64 -1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3))) (pow.f64 N 2))) (.f64 -1/3 (*.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))))
(+.f64 (.f64 -1/6 (/.f64 (+.f64 (.f64 2/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (+.f64 (.f64 2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))) (.f64 2 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))))))) (pow.f64 N 3))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3)) (.f64 -1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3))) (pow.f64 N 2))) (.f64 -1/3 (*.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3)))))
(+.f64 (.f64 -1/6 (/.f64 (+.f64 (.f64 2/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (+.f64 (.f64 2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))) (.f64 2 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))))))) (pow.f64 N 3))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3)) (.f64 -1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3))) (pow.f64 N 2))) (+.f64 (.f64 1/24 (/.f64 (+.f64 (.f64 -8/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))))) (+.f64 (.f64 -4/27 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 20)) 1/3)) (+.f64 (.f64 -2/27 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 20)) 1/3)) (+.f64 (.f64 8 (+.f64 (.f64 1/27 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 11)) 1/3)) (+.f64 (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))))) (.f64 -1/27 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 11)) 1/3))))) (.f64 -8/27 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 20)) 1/3)))))) (pow.f64 N 4))) (.f64 -1/3 (.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))))))
1
(-.f64 1 (*.f64 1/3 (/.f64 1 N)))
(-.f64 (+.f64 1 (.f64 2/9 (/.f64 1 (pow.f64 N 2)))) (.f64 1/3 (/.f64 1 N)))
(-.f64 (+.f64 1 (.f64 2/9 (/.f64 1 (pow.f64 N 2)))) (+.f64 (.f64 14/81 (/.f64 1 (pow.f64 N 3))) (*.f64 1/3 (/.f64 1 N))))
(pow.f64 (cbrt.f64 -1) 2)
(+.f64 (.f64 1/3 (.f64 (/.f64 1 N) (pow.f64 (*.f64 1 (cbrt.f64 -1)) 1/3))) (pow.f64 (cbrt.f64 -1) 2))
(+.f64 (.f64 -1/3 (/.f64 (+.f64 1 (.f64 1/3 (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 (pow.f64 N 2) (cbrt.f64 -1)))) (+.f64 (.f64 1/3 (.f64 (/.f64 1 N) (pow.f64 (.f64 1 (cbrt.f64 -1)) 1/3))) (pow.f64 (cbrt.f64 -1) 2)))
(+.f64 (.f64 -1/3 (/.f64 (-.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3) (+.f64 1 (.f64 1/3 (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))))) 1)) (.f64 (pow.f64 N 3) (cbrt.f64 -1)))) (+.f64 (.f64 -1/3 (/.f64 (+.f64 1 (.f64 1/3 (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 (pow.f64 N 2) (cbrt.f64 -1)))) (+.f64 (.f64 1/3 (.f64 (/.f64 1 N) (pow.f64 (.f64 1 (cbrt.f64 -1)) 1/3))) (pow.f64 (cbrt.f64 -1) 2))))

Outputs
(/.f64 1/3 N)
(-.f64 (.f64 1/3 (/.f64 1 N)) (.f64 1/6 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1/3 N) (/.f64 1/6 (*.f64 N N)))
(+.f64 (/.f64 1/3 N) (/.f64 -1/6 (*.f64 N N)))
(-.f64 (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 N 3))) (.f64 1/3 (/.f64 1 N))) (*.f64 1/6 (/.f64 1 (pow.f64 N 2))))
(+.f64 (/.f64 1/9 (pow.f64 N 3)) (-.f64 (/.f64 1/3 N) (/.f64 1/6 (*.f64 N N))))
(+.f64 (/.f64 1/3 N) (-.f64 (/.f64 1/9 (pow.f64 N 3)) (/.f64 1/6 (*.f64 N N))))
(+.f64 (/.f64 1/3 N) (+.f64 (/.f64 1/9 (pow.f64 N 3)) (/.f64 -1/6 (*.f64 N N))))
(-.f64 (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 N 3))) (.f64 1/3 (/.f64 1 N))) (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 2))) (.f64 1/12 (/.f64 1 (pow.f64 N 4)))))
(-.f64 (+.f64 (/.f64 1/9 (pow.f64 N 3)) (-.f64 (/.f64 1/3 N) (/.f64 1/6 (*.f64 N N)))) (/.f64 1/12 (pow.f64 N 4)))
(+.f64 (/.f64 1/3 N) (-.f64 (/.f64 1/9 (pow.f64 N 3)) (+.f64 (/.f64 1/6 (*.f64 N N)) (/.f64 1/12 (pow.f64 N 4)))))
(+.f64 (/.f64 1/3 N) (+.f64 (/.f64 1/9 (pow.f64 N 3)) (+.f64 (/.f64 -1/6 (*.f64 N N)) (/.f64 -1/12 (pow.f64 N 4)))))
(+.f64 (+.f64 (/.f64 1/3 N) (-.f64 (/.f64 1/9 (pow.f64 N 3)) (/.f64 1/6 (*.f64 N N)))) (/.f64 -1/12 (pow.f64 N 4)))
(.f64 -1/3 (.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3)))
(.f64 (.f64 -1/3 (/.f64 1 N)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))))
(*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 -1/3 N))
(*.f64 -1/3 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) N))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3)) (.f64 -1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3))) (pow.f64 N 2))) (.f64 -1/3 (*.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))))
(fma.f64 1/2 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) -1/3) (.f64 N N)) (.f64 (.f64 -1/3 (/.f64 1 N)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))))
(fma.f64 1/2 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) (/.f64 (.f64 N N) -1/3)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 -1/3 N)))
(fma.f64 -1/3 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) N) (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) -1/6) (.f64 N N)))
(.f64 (/.f64 -1/3 N) (+.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 (.f64 1/2 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)))) N)))
(+.f64 (.f64 -1/6 (/.f64 (+.f64 (.f64 2/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (+.f64 (.f64 2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))) (.f64 2 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))))))) (pow.f64 N 3))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3)) (.f64 -1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3))) (pow.f64 N 2))) (.f64 -1/3 (*.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3)))))
(fma.f64 -1/6 (/.f64 (+.f64 (/.f64 2/27 (pow.f64 (cbrt.f64 -1) 5)) (fma.f64 2/9 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) (.f64 2 (+.f64 (/.f64 1/27 (pow.f64 (cbrt.f64 -1) 2)) (.f64 -2/9 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))))) (pow.f64 N 3)) (fma.f64 1/2 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) -1/3) (.f64 N N)) (.f64 (.f64 -1/3 (/.f64 1 N)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))))))
(fma.f64 -1/6 (/.f64 (+.f64 (.f64 2 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) -5/27)) (.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 8/27)) (pow.f64 N 3)) (fma.f64 1/2 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) (/.f64 (.f64 N N) -1/3)) (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 -1/3 N))))
(fma.f64 -1/3 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) N) (fma.f64 -1/6 (/.f64 (fma.f64 2 (/.f64 -5/27 (pow.f64 (cbrt.f64 -1) 2)) (/.f64 8/27 (pow.f64 (cbrt.f64 -1) 5))) (pow.f64 N 3)) (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) -1/6) (.f64 N N))))
(fma.f64 -1/6 (/.f64 (fma.f64 2 (/.f64 -5/27 (pow.f64 (cbrt.f64 -1) 2)) (/.f64 8/27 (pow.f64 (cbrt.f64 -1) 5))) (pow.f64 N 3)) (.f64 (/.f64 -1/3 N) (+.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 (.f64 1/2 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)))) N))))
(+.f64 (.f64 -1/6 (/.f64 (+.f64 (.f64 2/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (+.f64 (.f64 2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))) (.f64 2 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)))))))) (pow.f64 N 3))) (+.f64 (.f64 1/2 (/.f64 (+.f64 (.f64 -2/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3)) (.f64 -1/9 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)) 1/3))) (pow.f64 N 2))) (+.f64 (.f64 1/24 (/.f64 (+.f64 (.f64 -8/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))))) (+.f64 (.f64 -4/27 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 20)) 1/3)) (+.f64 (.f64 -2/27 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 20)) 1/3)) (+.f64 (.f64 8 (+.f64 (.f64 1/27 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 11)) 1/3)) (+.f64 (.f64 -2/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (.f64 -2/9 (.f64 (pow.f64 1 1/3) (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))))) (.f64 -1/27 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 11)) 1/3))))) (.f64 -8/27 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 20)) 1/3)))))) (pow.f64 N 4))) (.f64 -1/3 (.f64 (/.f64 1 N) (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3))))))
(fma.f64 -1/6 (/.f64 (+.f64 (/.f64 2/27 (pow.f64 (cbrt.f64 -1) 5)) (fma.f64 2/9 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) (.f64 2 (+.f64 (/.f64 1/27 (pow.f64 (cbrt.f64 -1) 2)) (.f64 -2/9 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))))) (pow.f64 N 3)) (fma.f64 1/2 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) -1/3) (.f64 N N)) (fma.f64 1/24 (/.f64 (fma.f64 -8/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (+.f64 (/.f64 1/27 (pow.f64 (cbrt.f64 -1) 2)) (.f64 -2/9 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))) (fma.f64 -4/27 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 20))) (fma.f64 -2/27 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 20))) (fma.f64 8 (fma.f64 1/27 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 11))) (fma.f64 -2/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (+.f64 (/.f64 1/27 (pow.f64 (cbrt.f64 -1) 2)) (.f64 -2/9 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 11))) -1/27))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 20))) -8/27))))) (pow.f64 N 4)) (.f64 (.f64 -1/3 (/.f64 1 N)) (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)))))))
(fma.f64 -1/6 (/.f64 (+.f64 (.f64 2 (.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) -5/27)) (.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 8/27)) (pow.f64 N 3)) (fma.f64 1/2 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) (/.f64 (.f64 N N) -1/3)) (fma.f64 -1/3 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) N) (/.f64 1/24 (/.f64 (pow.f64 N 4) (fma.f64 -8/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) -5/27)) (+.f64 (fma.f64 8 (fma.f64 1/27 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 11))) (fma.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) -5/27)) -2/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 11))) -1/27))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 20))) -8/27)) (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 20))) -2/9))))))))
(fma.f64 -1/6 (/.f64 (fma.f64 2 (/.f64 -5/27 (pow.f64 (cbrt.f64 -1) 2)) (/.f64 8/27 (pow.f64 (cbrt.f64 -1) 5))) (pow.f64 N 3)) (fma.f64 -1/3 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) N) (fma.f64 1/24 (/.f64 (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 40/81) (+.f64 (.f64 8 (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2)) 10/81) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 11))) 0))) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 20))) -14/27))) (pow.f64 N 4)) (/.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10))) -1/6) (*.f64 N N)))))
(fma.f64 -1/6 (/.f64 (fma.f64 2 (/.f64 -5/27 (pow.f64 (cbrt.f64 -1) 2)) (/.f64 8/27 (pow.f64 (cbrt.f64 -1) 5))) (pow.f64 N 3)) (fma.f64 1/24 (/.f64 (+.f64 (.f64 (/.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (pow.f64 (cbrt.f64 -1) 2)) 40/81) (+.f64 (+.f64 0 (.f64 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 -5/27 (pow.f64 (cbrt.f64 -1) 2))) -16/3)) (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 20))) -14/27))) (pow.f64 N 4)) (.f64 (/.f64 -1/3 N) (+.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (/.f64 (.f64 1/2 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 10)))) N)))))
1
(-.f64 1 (*.f64 1/3 (/.f64 1 N)))
(-.f64 1 (/.f64 1/3 N))
(+.f64 1 (/.f64 -1/3 N))
(-.f64 (+.f64 1 (.f64 2/9 (/.f64 1 (pow.f64 N 2)))) (.f64 1/3 (/.f64 1 N)))
(+.f64 1 (-.f64 (/.f64 2/9 (*.f64 N N)) (/.f64 1/3 N)))
(+.f64 (/.f64 2/9 (*.f64 N N)) (+.f64 1 (/.f64 -1/3 N)))
(+.f64 (+.f64 1 (/.f64 -1/3 N)) (/.f64 2/9 (*.f64 N N)))
(+.f64 1 (+.f64 (/.f64 2/9 (*.f64 N N)) (/.f64 -1/3 N)))
(-.f64 (+.f64 1 (.f64 2/9 (/.f64 1 (pow.f64 N 2)))) (+.f64 (.f64 14/81 (/.f64 1 (pow.f64 N 3))) (*.f64 1/3 (/.f64 1 N))))
(-.f64 (+.f64 1 (/.f64 2/9 (*.f64 N N))) (+.f64 (/.f64 1/3 N) (/.f64 14/81 (pow.f64 N 3))))
(+.f64 (+.f64 1 (-.f64 (/.f64 2/9 (*.f64 N N)) (/.f64 14/81 (pow.f64 N 3)))) (/.f64 -1/3 N))
(+.f64 (/.f64 2/9 (*.f64 N N)) (+.f64 (+.f64 1 (/.f64 -1/3 N)) (/.f64 -14/81 (pow.f64 N 3))))
(+.f64 1 (+.f64 (/.f64 2/9 (*.f64 N N)) (+.f64 (/.f64 -1/3 N) (/.f64 -14/81 (pow.f64 N 3)))))
(pow.f64 (cbrt.f64 -1) 2)
(+.f64 (.f64 1/3 (.f64 (/.f64 1 N) (pow.f64 (*.f64 1 (cbrt.f64 -1)) 1/3))) (pow.f64 (cbrt.f64 -1) 2))
(+.f64 (pow.f64 (cbrt.f64 -1) 2) (*.f64 (/.f64 1/3 N) (cbrt.f64 (cbrt.f64 -1))))
(fma.f64 1/3 (/.f64 (cbrt.f64 (cbrt.f64 -1)) N) (pow.f64 (cbrt.f64 -1) 2))
(+.f64 (.f64 -1/3 (/.f64 (+.f64 1 (.f64 1/3 (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 (pow.f64 N 2) (cbrt.f64 -1)))) (+.f64 (.f64 1/3 (.f64 (/.f64 1 N) (pow.f64 (.f64 1 (cbrt.f64 -1)) 1/3))) (pow.f64 (cbrt.f64 -1) 2)))
(fma.f64 -1/3 (/.f64 (+.f64 1 (.f64 1/3 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))))) (.f64 (.f64 N N) (cbrt.f64 -1))) (+.f64 (pow.f64 (cbrt.f64 -1) 2) (.f64 (/.f64 1/3 N) (cbrt.f64 (cbrt.f64 -1)))))
(fma.f64 -1/3 (/.f64 (fma.f64 1/3 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) 1) (.f64 N (.f64 N (cbrt.f64 -1)))) (fma.f64 1/3 (/.f64 (cbrt.f64 (cbrt.f64 -1)) N) (pow.f64 (cbrt.f64 -1) 2)))
(fma.f64 1/3 (/.f64 (cbrt.f64 (cbrt.f64 -1)) N) (fma.f64 (/.f64 (/.f64 -1/3 N) N) (/.f64 (fma.f64 1/3 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) 1) (cbrt.f64 -1)) (pow.f64 (cbrt.f64 -1) 2)))
(fma.f64 1/3 (/.f64 (cbrt.f64 (cbrt.f64 -1)) N) (fma.f64 -1/3 (/.f64 (fma.f64 1/3 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) 1) (.f64 N (.f64 N (cbrt.f64 -1)))) (pow.f64 (cbrt.f64 -1) 2)))
(+.f64 (.f64 -1/3 (/.f64 (-.f64 (.f64 1/27 (/.f64 1 (pow.f64 (cbrt.f64 -1) 2))) (+.f64 (.f64 2/3 (.f64 (pow.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5)) 1/3) (+.f64 1 (.f64 1/3 (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))))) 1)) (.f64 (pow.f64 N 3) (cbrt.f64 -1)))) (+.f64 (.f64 -1/3 (/.f64 (+.f64 1 (.f64 1/3 (pow.f64 (/.f64 1 (cbrt.f64 -1)) 1/3))) (.f64 (pow.f64 N 2) (cbrt.f64 -1)))) (+.f64 (.f64 1/3 (.f64 (/.f64 1 N) (pow.f64 (.f64 1 (cbrt.f64 -1)) 1/3))) (pow.f64 (cbrt.f64 -1) 2))))
(fma.f64 -1/3 (/.f64 (-.f64 (/.f64 1/27 (pow.f64 (cbrt.f64 -1) 2)) (fma.f64 2/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (+.f64 1 (.f64 1/3 (cbrt.f64 (/.f64 1 (cbrt.f64 -1)))))) 1)) (.f64 (pow.f64 N 3) (cbrt.f64 -1))) (fma.f64 -1/3 (/.f64 (+.f64 1 (.f64 1/3 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))))) (.f64 (.f64 N N) (cbrt.f64 -1))) (+.f64 (pow.f64 (cbrt.f64 -1) 2) (*.f64 (/.f64 1/3 N) (cbrt.f64 (cbrt.f64 -1))))))
(fma.f64 -1/3 (/.f64 (-.f64 (/.f64 1/27 (pow.f64 (cbrt.f64 -1) 2)) (fma.f64 2/3 (.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (fma.f64 1/3 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) 1)) 1)) (.f64 (pow.f64 N 3) (cbrt.f64 -1))) (fma.f64 -1/3 (/.f64 (fma.f64 1/3 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) 1) (.f64 N (.f64 N (cbrt.f64 -1)))) (fma.f64 1/3 (/.f64 (cbrt.f64 (cbrt.f64 -1)) N) (pow.f64 (cbrt.f64 -1) 2))))
(+.f64 (fma.f64 1/3 (/.f64 (cbrt.f64 (cbrt.f64 -1)) N) (pow.f64 (cbrt.f64 -1) 2)) (.f64 (/.f64 -1/3 (cbrt.f64 -1)) (+.f64 (/.f64 (fma.f64 1/3 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) 1) (.f64 N N)) (/.f64 (-.f64 (/.f64 1/27 (pow.f64 (cbrt.f64 -1) 2)) (fma.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) (*.f64 (fma.f64 1/3 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) 1) 2/3) 1)) (pow.f64 N 3)))))
(fma.f64 -1/3 (+.f64 (/.f64 (fma.f64 1/3 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) 1) (.f64 N (.f64 N (cbrt.f64 -1)))) (/.f64 (+.f64 -1/27 (/.f64 (fma.f64 (fma.f64 1/3 (cbrt.f64 (/.f64 1 (cbrt.f64 -1))) 1) (*.f64 (cbrt.f64 (/.f64 1 (pow.f64 (cbrt.f64 -1) 5))) -2/3) -1) (cbrt.f64 -1))) (pow.f64 N 3))) (fma.f64 1/3 (/.f64 (cbrt.f64 (cbrt.f64 -1)) N) (pow.f64 (cbrt.f64 -1) 2)))

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (+.f64 N 1/2))
✓	0.0b	(/.f64 1 (+.f64 N 1/2))

Compiler

Compiled 12 to 9 computations (25% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(/.f64 1 (+.f64 N 1/2))
1.0ms	N	@	inf	(/.f64 1 (+.f64 N 1/2))
1.0ms	N	@	-inf	(/.f64 1 (+.f64 N 1/2))

rewrite81.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

622×	`pow1_binary64`
582×	`add-log-exp_binary64`
582×	`log1p-expm1-u_binary64`
582×	`expm1-log1p-u_binary64`
572×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	130	7
2	1574	7

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(/.f64 1 (+.f64 N 1/2))

Outputs

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

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

729×	`fma-def_binary64`
724×	`associate-l_binary64`
724×	`distribute-neg-frac_binary64`
503×	`associate-r_binary64`
415×	`times-frac_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	183
1	93	179
2	231	177
3	623	171
4	1879	168
5	7284	168

Stop Event

1×	node limit

Counts

34 → 36

Calls

Call 1

Inputs
2
(+.f64 2 (*.f64 -4 N))
(+.f64 (.f64 8 (pow.f64 N 2)) (+.f64 2 (.f64 -4 N)))
(+.f64 (.f64 8 (pow.f64 N 2)) (+.f64 2 (+.f64 (.f64 -4 N) (*.f64 -16 (pow.f64 N 3)))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/4 (/.f64 1 (pow.f64 N 3)))) (.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/4 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/4 (/.f64 1 (pow.f64 N 3)))) (.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/4 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))

Outputs
2
(+.f64 2 (*.f64 -4 N))
(fma.f64 -4 N 2)
(+.f64 (.f64 8 (pow.f64 N 2)) (+.f64 2 (.f64 -4 N)))
(fma.f64 8 (.f64 N N) (+.f64 2 (.f64 -4 N)))
(fma.f64 8 (*.f64 N N) (fma.f64 -4 N 2))
(fma.f64 -4 N (fma.f64 8 (*.f64 N N) 2))
(fma.f64 N (fma.f64 N 8 -4) 2)
(+.f64 (.f64 8 (pow.f64 N 2)) (+.f64 2 (+.f64 (.f64 -4 N) (*.f64 -16 (pow.f64 N 3)))))
(fma.f64 8 (.f64 N N) (+.f64 2 (fma.f64 -4 N (.f64 -16 (pow.f64 N 3)))))
(+.f64 (fma.f64 8 (.f64 N N) (fma.f64 -4 N 2)) (.f64 -16 (pow.f64 N 3)))
(fma.f64 N (*.f64 N 8) (fma.f64 -16 (pow.f64 N 3) (fma.f64 -4 N 2)))
(fma.f64 N (*.f64 N (fma.f64 N -16 8)) (fma.f64 -4 N 2))
(fma.f64 N (fma.f64 N (fma.f64 N -16 8) -4) 2)
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 (/.f64 -1/2 N) N))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/4 (/.f64 1 (pow.f64 N 3)))) (.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/4 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))
(+.f64 (+.f64 (/.f64 1 N) (/.f64 1/4 (pow.f64 N 3))) (/.f64 -1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/4 (pow.f64 N 3)) (/.f64 -1/2 (*.f64 N N))))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/4 (pow.f64 N 3)) (/.f64 (/.f64 -1/2 N) N)))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/4 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/4 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/8 (pow.f64 N 4))))
(-.f64 (+.f64 (+.f64 (/.f64 1 N) (/.f64 1/4 (pow.f64 N 3))) (/.f64 -1/2 (*.f64 N N))) (/.f64 1/8 (pow.f64 N 4)))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/4 (pow.f64 N 3)) (-.f64 (/.f64 -1/2 (*.f64 N N)) (/.f64 1/8 (pow.f64 N 4)))))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/4 (pow.f64 N 3)) (-.f64 (/.f64 (/.f64 -1/2 N) N) (/.f64 1/8 (pow.f64 N 4)))))
(+.f64 (/.f64 1 N) (-.f64 (/.f64 -1/8 (pow.f64 N 4)) (.f64 (/.f64 1 (.f64 N N)) (-.f64 1/2 (/.f64 1/4 N)))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (/.f64 (/.f64 -1/2 N) N))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/4 (/.f64 1 (pow.f64 N 3)))) (.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/4 (pow.f64 N 3))) (/.f64 1/2 (*.f64 N N)))
(+.f64 (+.f64 (/.f64 1 N) (/.f64 1/4 (pow.f64 N 3))) (/.f64 -1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/4 (pow.f64 N 3)) (/.f64 -1/2 (*.f64 N N))))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/4 (pow.f64 N 3)) (/.f64 (/.f64 -1/2 N) N)))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/4 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/4 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/8 (pow.f64 N 4))))
(-.f64 (+.f64 (+.f64 (/.f64 1 N) (/.f64 1/4 (pow.f64 N 3))) (/.f64 -1/2 (*.f64 N N))) (/.f64 1/8 (pow.f64 N 4)))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/4 (pow.f64 N 3)) (-.f64 (/.f64 -1/2 (*.f64 N N)) (/.f64 1/8 (pow.f64 N 4)))))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/4 (pow.f64 N 3)) (-.f64 (/.f64 (/.f64 -1/2 N) N) (/.f64 1/8 (pow.f64 N 4)))))
(+.f64 (/.f64 1 N) (-.f64 (/.f64 -1/8 (pow.f64 N 4)) (.f64 (/.f64 1 (.f64 N N)) (-.f64 1/2 (/.f64 1/4 N)))))

localize32.0ms (0.4%)

Local error

Found 6 expressions with local error:

New	Error	Program
	23.5b	(/.f64 (-.f64 (.f64 N (.f64 N 2)) N) (.f64 N (.f64 N (*.f64 N 2))))
	0.1b	(.f64 N (.f64 N (*.f64 N 2)))
	0.0b	(-.f64 (.f64 N (.f64 N 2)) N)
✓	0.0b	(-.f64 (.f64 N (.f64 N 2)) N)
✓	0.1b	(.f64 N (.f64 N (*.f64 N 2)))
✓	23.5b	(/.f64 (-.f64 (.f64 N (.f64 N 2)) N) (.f64 N (.f64 N (*.f64 N 2))))

Compiler

Compiled 40 to 24 computations (40% saved)

series9.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(/.f64 (-.f64 (.f64 N (.f64 N 2)) N) (.f64 N (.f64 N (*.f64 N 2))))
1.0ms	N	@	inf	(/.f64 (-.f64 (.f64 N (.f64 N 2)) N) (.f64 N (.f64 N (*.f64 N 2))))
1.0ms	N	@	-inf	(.f64 N (.f64 N (*.f64 N 2)))
1.0ms	N	@	inf	(.f64 N (.f64 N (*.f64 N 2)))
1.0ms	N	@	-inf	(/.f64 (-.f64 (.f64 N (.f64 N 2)) N) (.f64 N (.f64 N (*.f64 N 2))))

rewrite137.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

598×	`log-prod_binary64`
330×	`fma-def_binary64`
326×	`pow-prod-down_binary64`
247×	`pow2_binary64`
225×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	42
1	186	36
2	2914	30

Stop Event

1×	node limit

Counts

3 → 235

Calls

Call 1

Inputs
(/.f64 (-.f64 (.f64 N (.f64 N 2)) N) (.f64 N (.f64 N (*.f64 N 2))))
(.f64 N (.f64 N (*.f64 N 2)))
(-.f64 (.f64 N (.f64 N 2)) N)

Outputs

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

simplify93.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

615×	`associate-/l/_binary64`
536×	`unswap-sqr_binary64`
522×	`fma-def_binary64`
490×	`fma-neg_binary64`
429×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	323
1	46	323
2	88	323
3	214	305
4	640	305
5	2603	305
6	7905	305

Stop Event

1×	node limit

Counts

271 → 246

Calls

Call 1

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

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

localize11.0ms (0.1%)

Compiler: Compiled 8 to 3 computations (62.5% saved)

localize70.0ms (0.8%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.2b	(cbrt.f64 (+.f64 N 1))
	0.2b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 (cbrt.f64 N))))
	0.0b	(/.f64 (+.f64 N 1) N)
	0.0b	(log.f64 (cbrt.f64 N))
✓	0.6b	(cbrt.f64 N)
	2.6b	(log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2))
✓	2.7b	(-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 (cbrt.f64 N)))
✓	3.0b	(log.f64 (cbrt.f64 (+.f64 N 1)))

Compiler

Compiled 77 to 52 computations (32.5% saved)

series21.0ms (0.2%)

Counts

3 → 4

Calls

9 calls:

Time	Variable		Point	Expression
9.0ms	N	@	inf	(-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 (cbrt.f64 N)))
7.0ms	N	@	-inf	(-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 (cbrt.f64 N)))
1.0ms	N	@	0	(-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 (cbrt.f64 N)))
1.0ms	N	@	0	(log.f64 (cbrt.f64 (+.f64 N 1)))
1.0ms	N	@	inf	(log.f64 (cbrt.f64 (+.f64 N 1)))

rewrite61.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

946×	`pow1_binary64`
882×	`log1p-expm1-u_binary64`
882×	`expm1-log1p-u_binary64`
881×	`add-log-exp_binary64`
92×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	24
1	185	20
2	2407	20

Stop Event

1×	node limit

Counts

3 → 78

Calls

Call 1

Inputs
(log.f64 (cbrt.f64 (+.f64 N 1)))
(-.f64 (log.f64 (cbrt.f64 (+.f64 N 1))) (log.f64 (cbrt.f64 N)))
(cbrt.f64 N)

Outputs

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

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

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

simplify114.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

945×	`fma-def_binary64`
803×	`unswap-sqr_binary64`
581×	`distribute-lft-out_binary64`
553×	`*-commutative_binary64`
371×	`sqr-pow_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	56	58
2	128	55
3	406	47
4	1325	42
5	3159	42
6	5119	42
7	5256	42
8	5496	42
9	5780	42
10	6329	42
11	7149	42
12	7773	42

Stop Event

1×	node limit

Counts

82 → 85

Calls

Call 1

Inputs
(*.f64 1/3 N)
(+.f64 (.f64 1/3 N) (.f64 -1/6 (pow.f64 N 2)))
(+.f64 (.f64 1/3 N) (+.f64 (.f64 1/9 (pow.f64 N 3)) (*.f64 -1/6 (pow.f64 N 2))))
(+.f64 (.f64 1/3 N) (+.f64 (.f64 1/9 (pow.f64 N 3)) (+.f64 (.f64 -1/6 (pow.f64 N 2)) (.f64 -1/12 (pow.f64 N 4)))))

Outputs
(*.f64 1/3 N)
(+.f64 (.f64 1/3 N) (.f64 -1/6 (pow.f64 N 2)))
(fma.f64 1/3 N (.f64 -1/6 (.f64 N N)))
(fma.f64 1/3 N (.f64 N (.f64 N -1/6)))
(.f64 N (+.f64 1/3 (.f64 N -1/6)))
(*.f64 N (fma.f64 N -1/6 1/3))
(+.f64 (.f64 1/3 N) (+.f64 (.f64 1/9 (pow.f64 N 3)) (*.f64 -1/6 (pow.f64 N 2))))
(fma.f64 1/3 N (fma.f64 1/9 (pow.f64 N 3) (.f64 -1/6 (.f64 N N))))
(fma.f64 1/3 N (fma.f64 -1/6 (.f64 N N) (.f64 1/9 (pow.f64 N 3))))
(fma.f64 1/3 N (.f64 (.f64 N N) (+.f64 -1/6 (*.f64 N 1/9))))
(.f64 N (+.f64 1/3 (.f64 N (fma.f64 N 1/9 -1/6))))
(*.f64 N (fma.f64 N (fma.f64 N 1/9 -1/6) 1/3))
(+.f64 (.f64 1/3 N) (+.f64 (.f64 1/9 (pow.f64 N 3)) (+.f64 (.f64 -1/6 (pow.f64 N 2)) (.f64 -1/12 (pow.f64 N 4)))))
(fma.f64 1/3 N (fma.f64 1/9 (pow.f64 N 3) (fma.f64 -1/6 (.f64 N N) (.f64 -1/12 (pow.f64 N 4)))))
(fma.f64 1/3 N (fma.f64 -1/12 (pow.f64 N 4) (.f64 (.f64 N N) (+.f64 -1/6 (*.f64 N 1/9)))))
(fma.f64 -1/12 (pow.f64 N 4) (.f64 N (+.f64 1/3 (.f64 N (fma.f64 N 1/9 -1/6)))))
(.f64 N (+.f64 1/3 (.f64 N (fma.f64 N (fma.f64 N -1/12 1/9) -1/6))))

eval267.0ms (3.2%)

Compiler: Compiled 13605 to 9920 computations (27.1% saved)

prune69.0ms (0.8%)

Pruning

13 alts after pruning (5 fresh and 8 done)

	Pruned	Kept	Total
New	560	5	565
Fresh	0	0	0
Picked	1	0	1
Done	1	8	9
Total	562	13	575

Error

Counts

575 → 13

Alt Table

Click to see full alt table

Status	Error	Program
✓	27.9b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N))))
✓	29.0b	(-.f64 N (log.f64 N))
	61.9b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (.f64 (+.f64 (sqrt.f64 (.f64 (log1p.f64 N) 1/3)) (sqrt.f64 (log.f64 (cbrt.f64 N)))) (-.f64 (sqrt.f64 (*.f64 (log1p.f64 N) 1/3)) (sqrt.f64 (log.f64 (cbrt.f64 N))))))
✓	29.9b	(neg.f64 (log.f64 N))
	57.5b	2
✓	33.7b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
	57.1b	(-.f64 (+.f64 1 (/.f64 1 (+.f64 N 1/2))) 1)
✓	27.7b	(log.f64 (/.f64 (+.f64 N 1) N))
	28.2b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (-.f64 (*.f64 1/3 (log1p.f64 N)) (log.f64 (cbrt.f64 N))))
✓	32.7b	(/.f64 1 N)
✓	29.4b	(/.f64 1 (+.f64 N 1/2))
✓	27.9b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (log.f64 (/.f64 1 (cbrt.f64 (/.f64 N (+.f64 N 1))))))
	52.6b	(/.f64 (.f64 N (.f64 N 2)) (.f64 N (.f64 N (*.f64 N 2))))

Compiler

Compiled 155 to 116 computations (25.2% saved)

regimes50.0ms (0.6%)

Counts

24 → 2

Calls

Call 1

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

Outputs
(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
(log.f64 (/.f64 (+.f64 N 1) N))

Calls

3 calls:

22.0ms	N
11.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
10.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

Results

Error	Segments	Branch
0.0b	2	`N`
0.0b	2	`(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))`
0.0b	2	`(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))`

Compiler

Compiled 272 to 176 computations (35.3% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	5.588047358173753e-8	0.09734967481976753

Compiler

Compiled 12 to 9 computations (25% saved)

regimes20.0ms (0.2%)

Counts

15 → 2

Calls

Call 1

Inputs
2
(/.f64 1 N)
(/.f64 1 (+.f64 N 1/2))
(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
(-.f64 (+.f64 1 (/.f64 1 (+.f64 N 1/2))) 1)
(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))
(/.f64 (.f64 N (.f64 N 2)) (.f64 N (.f64 N (*.f64 N 2))))
(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
(/.f64 (-.f64 (.f64 N (.f64 N 2)) N) (.f64 N (.f64 N (*.f64 N 2))))
(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
(neg.f64 (log.f64 N))
(-.f64 N (log.f64 N))
(-.f64 N (log.f64 N))

Outputs
(-.f64 N (log.f64 N))
(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))

Calls

1 calls:

16.0ms

Results

Error	Segments	Branch
0.5b	2	`N`

Compiler

Compiled 124 to 80 computations (35.5% saved)

bsearch25.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
24.0ms	0.008572902970753304	9.073206425424452

Compiler

Compiled 12 to 9 computations (25% saved)

regimes17.0ms (0.2%)

Counts

13 → 2

Calls

Call 1

Inputs
2
(/.f64 1 N)
(/.f64 1 (+.f64 N 1/2))
(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
(-.f64 (+.f64 1 (/.f64 1 (+.f64 N 1/2))) 1)
(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))
(/.f64 (.f64 N (.f64 N 2)) (.f64 N (.f64 N (*.f64 N 2))))
(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
(/.f64 (-.f64 (.f64 N (.f64 N 2)) N) (.f64 N (.f64 N (*.f64 N 2))))
(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
(neg.f64 (log.f64 N))

Outputs
(neg.f64 (log.f64 N))
(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))

Calls

1 calls:

14.0ms

Results

Error	Segments	Branch
0.9b	2	`N`

Compiler

Compiled 116 to 79 computations (31.9% saved)

bsearch24.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
24.0ms	0.008572902970753304	9.073206425424452

Compiler

Compiled 12 to 9 computations (25% saved)

regimes10.0ms (0.1%)

Counts

12 → 1

Calls

Call 1

Inputs
2
(/.f64 1 N)
(/.f64 1 (+.f64 N 1/2))
(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
(-.f64 (+.f64 1 (/.f64 1 (+.f64 N 1/2))) 1)
(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
(/.f64 (-.f64 N (/.f64 (.f64 N 1/2) N)) (.f64 N N))
(/.f64 (.f64 N (.f64 N 2)) (.f64 N (.f64 N (*.f64 N 2))))
(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
(/.f64 (-.f64 (.f64 N (.f64 N 2)) N) (.f64 N (.f64 N (*.f64 N 2))))
(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))

Outputs
(/.f64 1 (+.f64 N 1/2))

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
29.4b	1	`N`

Compiler

Compiled 113 to 77 computations (31.9% saved)

regimes8.0ms (0.1%)

Accuracy

Total -30.9b remaining (-104%)

Threshold costs -30.9b (-104%)

Counts

2 → 2

Calls

Call 1

Inputs
2
(/.f64 1 N)

Outputs
2
(/.f64 1 N)

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
29.7b	2	`N`

Compiler

Compiled 7 to 5 computations (28.6% saved)

bsearch23.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
23.0ms	0.008572902970753304	9.073206425424452

Compiler

Compiled 12 to 9 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	124
1	43	124
2	47	124
3	48	124

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 944473296573929/9444732965739290427392) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)) (log.f64 (/.f64 (+.f64 N 1) N)))
(if (<=.f64 N 158142147070230528/18446744073709551616) (-.f64 N (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)))
(if (<=.f64 N 158142147070230528/18446744073709551616) (neg.f64 (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)))
(/.f64 1 (+.f64 N 1/2))
(if (<=.f64 N 158142147070230528/18446744073709551616) 2 (/.f64 1 N))
2

Outputs
(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 944473296573929/9444732965739290427392) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)) (log.f64 (/.f64 (+.f64 N 1) N)))
(if (<=.f64 N 158142147070230528/18446744073709551616) (-.f64 N (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)))
(if (<=.f64 N 4826115328071/562949953421312) (-.f64 N (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)))
(if (<=.f64 N 158142147070230528/18446744073709551616) (neg.f64 (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)))
(if (<=.f64 N 4826115328071/562949953421312) (neg.f64 (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)))
(/.f64 1 (+.f64 N 1/2))
(if (<=.f64 N 158142147070230528/18446744073709551616) 2 (/.f64 1 N))
(if (<=.f64 N 4826115328071/562949953421312) 2 (/.f64 1 N))
2

Compiler

Compiled 90 to 66 computations (26.7% saved)

soundness105.0ms (1.3%)

Algorithm

3×	egg-herbie

Rules

746×	`fma-def_binary64`
701×	`associate-l_binary64`
458×	`fma-neg_binary64`
427×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	33	8
5	50	8
6	87	8
7	123	8
8	170	8
9	206	8
10	232	8
11	234	8
0	36	192
1	95	188
2	237	185
3	646	181
4	2109	181
0	7	11
1	12	8
2	17	8
3	24	8
4	33	8
5	50	8
6	87	8
7	123	8
8	170	8
9	206	8
10	232	8
11	234	8

Stop Event

1×	saturated
1×	node limit
1×	saturated

Compiler

Compiled 226 to 180 computations (20.4% saved)

end52.0ms (0.6%)

Compiler: Compiled 85 to 59 computations (30.6% saved)