Details

analyze3.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	50%	25%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.1s (32.9%)

Results

958.0ms	2013×	body	1024	valid
784.0ms	4959×	body	256	valid
237.0ms	1015×	body	512	valid
153.0ms	269×	body	2048	valid

preprocess42.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	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)

simplify141.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 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

29.5b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	29.5b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.2b	(-.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	@	0	(-.f64 (log1p.f64 N) (log.f64 N))
1.0ms	N	@	inf	(-.f64 (log1p.f64 N) (log.f64 N))
1.0ms	N	@	-inf	(-.f64 (log1p.f64 N) (log.f64 N))

rewrite69.0ms (1.1%)

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)))))))

simplify55.0ms (0.8%)

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))))

eval12.0ms (0.2%)

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

prune21.0ms (0.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	38	12	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	13	51

Error

0.1b

Counts

51 → 13

Alt Table

Click to see full alt table

Status	Error	Program
	29.9b	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
	32.5b	(neg.f64 (log.f64 N))
	60.5b	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
▶	31.2b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
▶	29.3b	(log.f64 (/.f64 (+.f64 N 1) N))
	31.7b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
	29.7b	(pow.f64 (sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 2)
▶	30.8b	(/.f64 1 N)
▶	31.6b	(-.f64 N (log.f64 N))
	29.5b	(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) (+.f64 (log1p.f64 N) (log.f64 N)))
✓	29.5b	(-.f64 (log1p.f64 N) (log.f64 N))
	31.4b	(+.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))))
▶	31.4b	(-.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)))))

Compiler

Compiled 302 to 214 computations (29.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 N 1) N)
✓	3.1b	(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
1.0ms	N	@	0	(log.f64 (/.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	(/.f64 (+.f64 N 1) N)
0.0ms	N	@	inf	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite64.0ms (1%)

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)))))))

simplify51.0ms (0.8%)

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)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))
✓	0.3b	(/.f64 1/3 N)
✓	0.6b	(/.f64 1 (*.f64 N N))

Compiler

Compiled 50 to 32 computations (36% saved)

series6.0ms (0.1%)

Counts

4 → 36

Calls

12 calls:

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

rewrite105.0ms (1.6%)

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
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(pow.f64 N -1))))))

simplify65.0ms (1%)

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%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 N (log.f64 N))

Compiler

Compiled 8 to 3 computations (62.5% saved)

series8.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	N	@	0	(-.f64 N (log.f64 N))
2.0ms	N	@	-inf	(-.f64 N (log.f64 N))
1.0ms	N	@	inf	(-.f64 N (log.f64 N))

rewrite45.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

508×	`pow1_binary64`
491×	`add-sqr-sqrt_binary64`
475×	`add-log-exp_binary64`
475×	`log1p-expm1-u_binary64`
475×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	88	6
2	1262	6

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs

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

simplify159.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1741×	`fma-neg_binary64`
851×	`distribute-rgt-in_binary64`
627×	`fma-def_binary64`
525×	`distribute-lft-in_binary64`
297×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	79
1	37	61
2	72	61
3	141	61
4	331	61
5	941	61
6	3007	61
7	4269	61
8	4843	61
9	5305	61
10	5863	61
11	5960	61
12	7638	61
13	7666	61
14	7682	61
15	7718	61
16	7998	61

Stop Event

1×	node limit

Counts

47 → 42

Calls

Call 1

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

localize46.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (pow.f64 N 4))
✓	0.4b	(/.f64 1 (pow.f64 N 3))
✓	0.6b	(/.f64 1 (pow.f64 N 2))
✓	21.5b	(-.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)))))

Compiler

Compiled 110 to 91 computations (17.3% saved)

series5.0ms (0.1%)

Counts

4 → 9

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(-.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)))))
1.0ms	N	@	0	(/.f64 1 (pow.f64 N 4))
1.0ms	N	@	0	(/.f64 1 (pow.f64 N 3))
0.0ms	N	@	inf	(-.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)))))
0.0ms	N	@	-inf	(/.f64 1 (pow.f64 N 3))

rewrite106.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

657×	`fma-neg_binary64`
357×	`expm1-udef_binary64`
357×	`log1p-udef_binary64`
238×	`add-sqr-sqrt_binary64`
228×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	41
1	516	39
2	6727	39

Stop Event

1×	node limit

Counts

4 → 163

Calls

Call 1

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

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

simplify51.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

838×	`distribute-neg-frac_binary64`
453×	`times-frac_binary64`
420×	`distribute-rgt-neg-in_binary64`
384×	`distribute-lft-neg-in_binary64`
339×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	126
1	74	126
2	157	126
3	361	126
4	1216	126
5	5333	126

Stop Event

1×	node limit

Counts

172 → 173

Calls

Call 1

Inputs
(/.f64 -1/4 (pow.f64 N 4))
(-.f64 (.f64 1/3 (/.f64 1 (pow.f64 N 3))) (.f64 1/4 (/.f64 1 (pow.f64 N 4))))
(-.f64 (.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 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))))

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

eval225.0ms (3.4%)

Compiler: Compiled 10683 to 7972 computations (25.4% saved)

prune78.0ms (1.2%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	487	11	498
Fresh	4	3	7
Picked	1	0	1
Done	3	2	5
Total	495	16	511

Error

0.1b

Counts

511 → 16

Alt Table

Click to see full alt table

Status	Error	Program
	61.0b	N
▶	29.3b	(log.f64 (+.f64 1 (/.f64 1 N)))
✓	31.6b	(-.f64 N (log.f64 N))
	32.5b	(neg.f64 (log.f64 N))
	29.5b	(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) (+.f64 (log1p.f64 N) (log.f64 N)))
	60.5b	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
▶	31.7b	(-.f64 (/.f64 (/.f64 -1/2 N) N) (/.f64 -1 N))
▶	29.4b	(+.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))) (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))))
✓	30.8b	(/.f64 1 N)
	31.4b	(+.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))))
	29.9b	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
	31.2b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
	52.5b	(pow.f64 (pow.f64 (-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/4 (pow.f64 N -4) (/.f64 1/2 (*.f64 N N)))) 3) 1/3)
▶	53.0b	(/.f64 (fma.f64 N (neg.f64 N) (.f64 (neg.f64 N) (+.f64 (/.f64 1/3 N) -1/2))) (.f64 (neg.f64 N) (*.f64 N N)))
	29.7b	(pow.f64 (sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 2)
▶	34.2b	(exp.f64 (log.f64 (-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/4 (pow.f64 N -4) (/.f64 1/2 (*.f64 N N))))))

Compiler

Compiled 393 to 273 computations (30.5% saved)

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.1b	(log.f64 (+.f64 1 (/.f64 1 N)))

Compiler

Compiled 17 to 13 computations (23.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite46.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

585×	`pow1_binary64`
545×	`add-log-exp_binary64`
545×	`log1p-expm1-u_binary64`
545×	`expm1-log1p-u_binary64`
534×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	125	6
2	1529	6

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

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

Outputs

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

simplify40.0ms (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	36	192
1	95	188
2	237	185
3	646	181
4	2109	181

Stop Event

1×	node limit

Counts

32 → 35

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))))

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (/.f64 -1/2 N) N) (/.f64 -1 N))
✓	0.2b	(/.f64 (/.f64 -1/2 N) N)

Compiler

Compiled 24 to 16 computations (33.3% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite73.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

951×	`prod-diff_binary64`
445×	`log-prod_binary64`
304×	`fma-def_binary64`
239×	`pow2_binary64`
237×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	189	17
2	2892	17

Stop Event

1×	node limit

Counts

2 → 211

Calls

Call 1

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

Outputs

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

simplify46.0ms (0.7%)

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	216
1	26	216
2	46	216
3	100	216
4	263	216
5	947	216
6	5090	216

Stop Event

1×	node limit

Counts

235 → 216

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 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))

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (neg.f64 N) (.f64 N N))
✓	0.2b	(*.f64 (neg.f64 N) (+.f64 (/.f64 1/3 N) -1/2))
	0.3b	(/.f64 1/3 N)
✓	21.6b	(/.f64 (fma.f64 N (neg.f64 N) (.f64 (neg.f64 N) (+.f64 (/.f64 1/3 N) -1/2))) (.f64 (neg.f64 N) (*.f64 N N)))

Compiler

Compiled 62 to 30 computations (51.6% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite108.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

640×	`prod-diff_binary64`
590×	`log-prod_binary64`
219×	`egg-rr`
212×	`fma-def_binary64`
212×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	50
1	282	33
2	4267	33

Stop Event

1×	node limit

Counts

3 → 279

Calls

Call 1

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

Outputs

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

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

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

536×	`unswap-sqr_binary64`
456×	`associate-/r/_binary64`
446×	`fma-def_binary64`
437×	`distribute-neg-frac_binary64`
358×	`associate-l_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	26	315
1	66	315
2	137	315
3	290	315
4	812	315
5	3377	303
6	7581	303

Stop Event

1×	node limit

Counts

315 → 294

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

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

localize18.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 N 1) N)
✓	0.1b	(sqrt.f64 (/.f64 (+.f64 N 1) N))
✓	3.2b	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))

Compiler

Compiled 39 to 27 computations (30.8% saved)

series5.0ms (0.1%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	N	@	0	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
1.0ms	N	@	-inf	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
1.0ms	N	@	inf	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
0.0ms	N	@	0	(sqrt.f64 (/.f64 (+.f64 N 1) N))
0.0ms	N	@	-inf	(sqrt.f64 (/.f64 (+.f64 N 1) N))

rewrite64.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

755×	`pow1_binary64`
705×	`log1p-expm1-u_binary64`
705×	`expm1-log1p-u_binary64`
704×	`add-log-exp_binary64`
689×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	147	20
2	1946	20

Stop Event

1×	node limit

Counts

2 → 53

Calls

Call 1

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

Outputs

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

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

simplify60.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

742×	`div-sub_binary64`
705×	`times-frac_binary64`
537×	`fma-def_binary64`
494×	`associate-/l/_binary64`
277×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	68	337
1	201	233
2	645	225
3	2041	225
4	7900	225

Stop Event

1×	node limit

Counts

69 → 83

Calls

Call 1

Inputs
(/.f64 1/2 N)
(-.f64 (.f64 1/2 (/.f64 1 N)) (.f64 1/4 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 3))) (.f64 1/2 (/.f64 1 N))) (*.f64 1/4 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 3))) (.f64 1/2 (/.f64 1 N))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 N 4))) (.f64 1/4 (/.f64 1 (pow.f64 N 2)))))
(log.f64 (pow.f64 (sqrt.f64 -1) 2))
(-.f64 (log.f64 (pow.f64 (sqrt.f64 -1) 2)) (.f64 1/2 (/.f64 1 (.f64 N (pow.f64 (sqrt.f64 -1) 2)))))
(-.f64 (log.f64 (pow.f64 (sqrt.f64 -1) 2)) (+.f64 (.f64 1/2 (/.f64 1 (.f64 N (pow.f64 (sqrt.f64 -1) 2)))) (.f64 1/4 (/.f64 1 (.f64 (pow.f64 N 2) (pow.f64 (sqrt.f64 -1) 4))))))
(-.f64 (log.f64 (pow.f64 (sqrt.f64 -1) 2)) (+.f64 (.f64 1/2 (/.f64 1 (.f64 N (pow.f64 (sqrt.f64 -1) 2)))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 N 2) (pow.f64 (sqrt.f64 -1) 4)))) (.f64 1/6 (/.f64 1 (.f64 (pow.f64 N 3) (pow.f64 (sqrt.f64 -1) 6)))))))
1
(+.f64 1 (*.f64 1/2 (/.f64 1 N)))
(-.f64 (+.f64 1 (.f64 1/2 (/.f64 1 N))) (.f64 1/8 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 N 3))) (+.f64 1 (.f64 1/2 (/.f64 1 N)))) (*.f64 1/8 (/.f64 1 (pow.f64 N 2))))
(pow.f64 (sqrt.f64 -1) 2)
(-.f64 (pow.f64 (sqrt.f64 -1) 2) (*.f64 1/2 (/.f64 1 N)))
(-.f64 (pow.f64 (sqrt.f64 -1) 2) (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 N 2) (pow.f64 (sqrt.f64 -1) 2)))) (*.f64 1/2 (/.f64 1 N))))
(-.f64 (pow.f64 (sqrt.f64 -1) 2) (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 N 2) (pow.f64 (sqrt.f64 -1) 2)))) (+.f64 (.f64 1/2 (/.f64 1 N)) (.f64 1/16 (/.f64 1 (*.f64 (pow.f64 N 3) (pow.f64 (sqrt.f64 -1) 4)))))))

Outputs
(/.f64 1/2 N)
(-.f64 (.f64 1/2 (/.f64 1 N)) (.f64 1/4 (/.f64 1 (pow.f64 N 2))))
(-.f64 (/.f64 1/2 N) (/.f64 1/4 (*.f64 N N)))
(+.f64 (/.f64 1/2 N) (/.f64 -1/4 (*.f64 N N)))
(-.f64 (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 3))) (.f64 1/2 (/.f64 1 N))) (*.f64 1/4 (/.f64 1 (pow.f64 N 2))))
(+.f64 (/.f64 1/6 (pow.f64 N 3)) (-.f64 (/.f64 1/2 N) (/.f64 1/4 (*.f64 N N))))
(+.f64 (/.f64 1/2 N) (-.f64 (/.f64 1/6 (pow.f64 N 3)) (/.f64 1/4 (*.f64 N N))))
(+.f64 (/.f64 1/2 N) (+.f64 (/.f64 1/6 (pow.f64 N 3)) (/.f64 -1/4 (*.f64 N N))))
(-.f64 (+.f64 (.f64 1/6 (/.f64 1 (pow.f64 N 3))) (.f64 1/2 (/.f64 1 N))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 N 4))) (.f64 1/4 (/.f64 1 (pow.f64 N 2)))))
(+.f64 (/.f64 1/6 (pow.f64 N 3)) (-.f64 (/.f64 1/2 N) (+.f64 (/.f64 1/4 (*.f64 N N)) (/.f64 1/8 (pow.f64 N 4)))))
(+.f64 (/.f64 1/2 N) (-.f64 (/.f64 1/6 (pow.f64 N 3)) (+.f64 (/.f64 1/8 (pow.f64 N 4)) (/.f64 1/4 (*.f64 N N)))))
(-.f64 (+.f64 (/.f64 1/2 N) (/.f64 1/6 (pow.f64 N 3))) (-.f64 (/.f64 1/8 (pow.f64 N 4)) (/.f64 -1/4 (*.f64 N N))))
(+.f64 (/.f64 -1/4 (.f64 N N)) (+.f64 (/.f64 1/2 N) (.f64 (/.f64 1 (pow.f64 N 3)) (-.f64 1/6 (/.f64 1/8 N)))))
(log.f64 (pow.f64 (sqrt.f64 -1) 2))
(log.f64 -1)
(-.f64 (log.f64 (pow.f64 (sqrt.f64 -1) 2)) (.f64 1/2 (/.f64 1 (.f64 N (pow.f64 (sqrt.f64 -1) 2)))))
(-.f64 (log.f64 (pow.f64 (sqrt.f64 -1) 2)) (/.f64 1/2 (*.f64 N (pow.f64 (sqrt.f64 -1) 2))))
(-.f64 (log.f64 -1) (/.f64 -1/2 N))
(+.f64 (/.f64 1/2 N) (log.f64 -1))
(-.f64 (log.f64 (pow.f64 (sqrt.f64 -1) 2)) (+.f64 (.f64 1/2 (/.f64 1 (.f64 N (pow.f64 (sqrt.f64 -1) 2)))) (.f64 1/4 (/.f64 1 (.f64 (pow.f64 N 2) (pow.f64 (sqrt.f64 -1) 4))))))
(-.f64 (log.f64 (pow.f64 (sqrt.f64 -1) 2)) (+.f64 (/.f64 1/2 (.f64 N (pow.f64 (sqrt.f64 -1) 2))) (/.f64 1/4 (.f64 (*.f64 N N) (pow.f64 (sqrt.f64 -1) 4)))))
(+.f64 (-.f64 (log.f64 -1) (/.f64 -1/2 N)) (/.f64 -1/4 (*.f64 N N)))
(+.f64 (log.f64 -1) (+.f64 (/.f64 1/2 N) (/.f64 -1/4 (*.f64 N N))))
(+.f64 (/.f64 1/2 N) (+.f64 (log.f64 -1) (/.f64 -1/4 (*.f64 N N))))
(-.f64 (log.f64 (pow.f64 (sqrt.f64 -1) 2)) (+.f64 (.f64 1/2 (/.f64 1 (.f64 N (pow.f64 (sqrt.f64 -1) 2)))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 N 2) (pow.f64 (sqrt.f64 -1) 4)))) (.f64 1/6 (/.f64 1 (.f64 (pow.f64 N 3) (pow.f64 (sqrt.f64 -1) 6)))))))
(-.f64 (log.f64 (pow.f64 (sqrt.f64 -1) 2)) (+.f64 (/.f64 1/2 (.f64 N (pow.f64 (sqrt.f64 -1) 2))) (+.f64 (/.f64 1/4 (.f64 (.f64 N N) (pow.f64 (sqrt.f64 -1) 4))) (/.f64 1/6 (.f64 (pow.f64 N 3) (pow.f64 (sqrt.f64 -1) 6))))))
(-.f64 (log.f64 -1) (+.f64 (/.f64 1/4 (.f64 N N)) (+.f64 (/.f64 -1/2 N) (/.f64 1/6 (.f64 (pow.f64 N 3) (pow.f64 (sqrt.f64 -1) 6))))))
(+.f64 (log.f64 -1) (+.f64 (/.f64 1/2 N) (+.f64 (/.f64 1/6 (pow.f64 N 3)) (/.f64 -1/4 (*.f64 N N)))))
(+.f64 (/.f64 1/6 (pow.f64 N 3)) (+.f64 (/.f64 1/2 N) (+.f64 (log.f64 -1) (/.f64 -1/4 (*.f64 N N)))))
1
(+.f64 1 (*.f64 1/2 (/.f64 1 N)))
(+.f64 1 (/.f64 1/2 N))
(-.f64 (+.f64 1 (.f64 1/2 (/.f64 1 N))) (.f64 1/8 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 1 (/.f64 1/2 N)) (/.f64 1/8 (*.f64 N N)))
(+.f64 (/.f64 1/2 N) (-.f64 1 (/.f64 1/8 (*.f64 N N))))
(+.f64 1 (+.f64 (/.f64 1/2 N) (/.f64 -1/8 (*.f64 N N))))
(-.f64 (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 N 3))) (+.f64 1 (.f64 1/2 (/.f64 1 N)))) (*.f64 1/8 (/.f64 1 (pow.f64 N 2))))
(+.f64 (/.f64 1/16 (pow.f64 N 3)) (-.f64 (+.f64 1 (/.f64 1/2 N)) (/.f64 1/8 (*.f64 N N))))
(+.f64 (+.f64 1 (/.f64 1/2 N)) (-.f64 (/.f64 1/16 (pow.f64 N 3)) (/.f64 1/8 (*.f64 N N))))
(+.f64 1 (+.f64 (/.f64 1/2 N) (+.f64 (/.f64 1/16 (pow.f64 N 3)) (/.f64 -1/8 (*.f64 N N)))))
(pow.f64 (sqrt.f64 -1) 2)
-1
(-.f64 (pow.f64 (sqrt.f64 -1) 2) (*.f64 1/2 (/.f64 1 N)))
(-.f64 (pow.f64 (sqrt.f64 -1) 2) (/.f64 1/2 N))
(+.f64 -1 (/.f64 -1/2 N))
(-.f64 -1 (/.f64 1/2 N))
(-.f64 (pow.f64 (sqrt.f64 -1) 2) (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 N 2) (pow.f64 (sqrt.f64 -1) 2)))) (*.f64 1/2 (/.f64 1 N))))
(-.f64 (pow.f64 (sqrt.f64 -1) 2) (+.f64 (/.f64 1/2 N) (/.f64 1/8 (.f64 (.f64 N N) (pow.f64 (sqrt.f64 -1) 2)))))
(+.f64 (-.f64 -1 (/.f64 -1/8 (*.f64 N N))) (/.f64 -1/2 N))
(+.f64 -1 (-.f64 (/.f64 -1/2 N) (/.f64 -1/8 (*.f64 N N))))
(+.f64 -1 (+.f64 (/.f64 -1/2 N) (/.f64 1/8 (*.f64 N N))))
(-.f64 (pow.f64 (sqrt.f64 -1) 2) (+.f64 (.f64 1/8 (/.f64 1 (.f64 (pow.f64 N 2) (pow.f64 (sqrt.f64 -1) 2)))) (+.f64 (.f64 1/2 (/.f64 1 N)) (.f64 1/16 (/.f64 1 (*.f64 (pow.f64 N 3) (pow.f64 (sqrt.f64 -1) 4)))))))
(-.f64 (pow.f64 (sqrt.f64 -1) 2) (+.f64 (/.f64 1/8 (.f64 (.f64 N N) (pow.f64 (sqrt.f64 -1) 2))) (+.f64 (/.f64 1/2 N) (/.f64 1/16 (*.f64 (pow.f64 N 3) (pow.f64 (sqrt.f64 -1) 4))))))
(-.f64 (-.f64 -1 (/.f64 -1/8 (*.f64 N N))) (+.f64 (/.f64 1/2 N) (/.f64 1/16 (pow.f64 N 3))))
(+.f64 -1 (+.f64 (-.f64 (/.f64 -1/2 N) (/.f64 -1/8 (*.f64 N N))) (/.f64 -1/16 (pow.f64 N 3))))
(-.f64 (/.f64 1/8 (*.f64 N N)) (+.f64 (+.f64 1 (/.f64 1/2 N)) (/.f64 1/16 (pow.f64 N 3))))

localize44.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N))
✓	0.5b	(/.f64 1/2 (*.f64 N N))
✓	2.7b	(exp.f64 (log.f64 (-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/4 (pow.f64 N -4) (/.f64 1/2 (*.f64 N N))))))
✓	21.5b	(-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/4 (pow.f64 N -4) (/.f64 1/2 (*.f64 N N))))

Compiler

Compiled 103 to 70 computations (32% saved)

series5.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	N	@	-inf	(fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N))
1.0ms	N	@	0	(fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N))
0.0ms	N	@	0	(-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/4 (pow.f64 N -4) (/.f64 1/2 (*.f64 N N))))
0.0ms	N	@	0	(/.f64 1/2 (*.f64 N N))
0.0ms	N	@	inf	(fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N))

rewrite123.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

799×	`prod-diff_binary64`
667×	`log-prod_binary64`
290×	`expm1-udef_binary64`
290×	`log1p-udef_binary64`
278×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	72
1	378	72
2	4372	72

Stop Event

1×	node limit

Counts

4 → 261

Calls

Call 1

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

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

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Rules

831×	`distribute-neg-frac_binary64`
453×	`times-frac_binary64`
421×	`distribute-rgt-neg-in_binary64`
340×	`associate-l_binary64`
335×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	654
1	80	654
2	178	654
3	423	654
4	1388	654
5	5928	654

Stop Event

1×	node limit

Counts

309 → 178

Calls

Call 1

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

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

eval676.0ms (10.4%)

Compiler: Compiled 25930 to 17516 computations (32.4% saved)

prune307.0ms (4.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	987	5	992
Fresh	6	3	9
Picked	1	0	1
Done	4	2	6
Total	998	10	1008

Error

0.0b

Counts

1008 → 10

Alt Table

Click to see full alt table

Status	Error	Program
	3.2b	(exp.f64 (log.f64 (log1p.f64 (/.f64 1 N))))
	61.0b	N
	32.5b	(neg.f64 (log.f64 N))
▶	31.7b	(/.f64 (+.f64 (/.f64 -1/2 N) 1) N)
▶	31.7b	(/.f64 1 (/.f64 N (+.f64 (/.f64 -1/2 N) 1)))
✓	31.7b	(-.f64 (/.f64 (/.f64 -1/2 N) N) (/.f64 -1 N))
▶	31.7b	(*.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 N) 1))
✓	30.8b	(/.f64 1 N)
▶	0.0b	(log1p.f64 (/.f64 1 N))
▶	31.2b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))

Compiler

Compiled 132 to 101 computations (23.5% saved)

localize11.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (/.f64 1 N))

Compiler

Compiled 10 to 7 computations (30% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	N	@	-inf	(log1p.f64 (/.f64 1 N))
1.0ms	N	@	0	(log1p.f64 (/.f64 1 N))
1.0ms	N	@	inf	(log1p.f64 (/.f64 1 N))

rewrite55.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

397×	`pow1_binary64`
383×	`add-sqr-sqrt_binary64`
375×	`*-un-lft-identity_binary64`
366×	`add-log-exp_binary64`
366×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	96	6
2	1059	6

Stop Event

1×	node limit

Counts

1 → 27

Calls

Call 1

Inputs
(log1p.f64 (/.f64 1 N))

Outputs

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

simplify74.0ms (1.1%)

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

39 → 42

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))))

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 14 computations (26.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite49.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

798×	`pow1_binary64`
749×	`add-log-exp_binary64`
749×	`log1p-expm1-u_binary64`
749×	`expm1-log1p-u_binary64`
736×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	155	10
2	2040	10

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

simplify50.0ms (0.8%)

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

43 → 36

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))

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 24 to 18 computations (25% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite61.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

896×	`pow1_binary64`
839×	`add-log-exp_binary64`
839×	`log1p-expm1-u_binary64`
839×	`expm1-log1p-u_binary64`
823×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	181	10
2	2419	10

Stop Event

1×	node limit

Counts

1 → 43

Calls

Call 1

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

Outputs

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

simplify46.0ms (0.7%)

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

55 → 48

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))

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 28 to 21 computations (25% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite76.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

925×	`pow1_binary64`
865×	`add-log-exp_binary64`
865×	`log1p-expm1-u_binary64`
865×	`expm1-log1p-u_binary64`
848×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	183	20
2	2458	20

Stop Event

1×	node limit

Counts

2 → 73

Calls

Call 1

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

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 (+.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 (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 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 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 (/.f64 1/4 (*.f64 N N)) (-.f64 1 (/.f64 -1/2 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 N (+.f64 (/.f64 1/4 (*.f64 N N)) -1)) (+.f64 (/.f64 -1/2 N) -1))))) (#(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 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))))))))

simplify62.0ms (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

97 → 92

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 (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)
	0.3b	(/.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	@	0	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
0.0ms	N	@	inf	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
0.0ms	N	@	inf	(/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)

rewrite102.0ms (1.6%)

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

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

simplify69.0ms (1.1%)

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))

eval216.0ms (3.3%)

Compiler: Compiled 7095 to 5384 computations (24.1% saved)

prune65.0ms (1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	441	2	443
Fresh	0	3	3
Picked	0	1	1
Done	4	2	6
Total	445	8	453

Error

Counts

453 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	3.2b	(exp.f64 (log.f64 (log1p.f64 (/.f64 1 N))))
	61.0b	N
✓	30.8b	(/.f64 1 N)
	27.4b	(/.f64 1 (+.f64 N 1/2))
✓	0.0b	(log1p.f64 (/.f64 1 N))
	32.5b	(neg.f64 (log.f64 N))
✓	31.2b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
	18.9b	(.f64 (pow.f64 (.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 2) (sqrt.f64 (log1p.f64 (/.f64 1 N)))) 1/3) (cbrt.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N)))))

Compiler

Compiled 64 to 51 computations (20.3% saved)

regimes38.0ms (0.6%)

Counts

32 → 1

Calls

Call 1

Inputs
N
(/.f64 1 N)
(/.f64 1 (+.f64 N 1/2))
(/.f64 (+.f64 (/.f64 -1/2 N) 1) N)
(/.f64 1 (/.f64 N (+.f64 (/.f64 -1/2 N) 1)))
(*.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 N) 1))
(-.f64 (/.f64 (/.f64 -1/2 N) N) (/.f64 -1 N))
(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
(neg.f64 (log.f64 N))
(neg.f64 (log.f64 N))
(log1p.f64 (/.f64 1 N))
(-.f64 N (log.f64 N))
(log.f64 (+.f64 1 (/.f64 1 N)))
(log.f64 (/.f64 (+.f64 N 1) N))
(/.f64 (fma.f64 N (neg.f64 N) (.f64 (neg.f64 N) (+.f64 (/.f64 1/3 N) -1/2))) (.f64 (neg.f64 N) (*.f64 N N)))
(+.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 (/.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 (log1p.f64 N) (log.f64 N))
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
(exp.f64 (log.f64 (log1p.f64 (/.f64 1 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)))))
(pow.f64 (sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 2)
(pow.f64 (sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 2)
(+.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))) (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))))
(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
(/.f64 (-.f64 (pow.f64 (log1p.f64 N) 2) (pow.f64 (log.f64 N) 2)) (+.f64 (log1p.f64 N) (log.f64 N)))
(exp.f64 (log.f64 (-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/4 (pow.f64 N -4) (/.f64 1/2 (*.f64 N N))))))
(pow.f64 (pow.f64 (-.f64 (fma.f64 1/3 (pow.f64 N -3) (/.f64 1 N)) (fma.f64 1/4 (pow.f64 N -4) (/.f64 1/2 (*.f64 N N)))) 3) 1/3)
(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
(.f64 (pow.f64 (.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 2) (sqrt.f64 (log1p.f64 (/.f64 1 N)))) 1/3) (cbrt.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N)))))

Outputs
(log1p.f64 (/.f64 1 N))

Calls

2 calls:

17.0ms	N
10.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

Results

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

Compiler

Compiled 359 to 232 computations (35.4% saved)

regimes19.0ms (0.3%)

Counts

12 → 2

Calls

Call 1

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

16.0ms

Results

Error	Segments	Branch
0.9b	2	`N`

Compiler

Compiled 89 to 61 computations (31.5% saved)

bsearch25.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
25.0ms	1.3683424085043775e-7	3.7720436768118772

Compiler

Compiled 12 to 9 computations (25% saved)

regimes10.0ms (0.1%)

Counts

10 → 1

Calls

Call 1

Inputs
N
(/.f64 1 N)
(/.f64 1 (+.f64 N 1/2))
(/.f64 (+.f64 (/.f64 -1/2 N) 1) N)
(/.f64 1 (/.f64 N (+.f64 (/.f64 -1/2 N) 1)))
(*.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 N) 1))
(-.f64 (/.f64 (/.f64 -1/2 N) N) (/.f64 -1 N))
(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
(+.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
27.4b	1	`N`

Compiler

Compiled 83 to 59 computations (28.9% saved)

regimes4.0ms (0.1%)

Accuracy

Total -30.2b remaining (-98.1%)

Threshold costs -30.2b (-98.1%)

Counts

2 → 1

Calls

Call 1

Inputs
N
(/.f64 1 N)

Outputs
(/.f64 1 N)

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
30.8b	1	`N`

Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	48
1	29	48
2	31	48
3	32	48

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(log1p.f64 (/.f64 1 N))
(if (<=.f64 N 5169451461608157/37778931862957161709568) (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))
(/.f64 1 N)
N

Outputs
(log1p.f64 (/.f64 1 N))
(if (<=.f64 N 5169451461608157/37778931862957161709568) (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))
(/.f64 1 N)
N

Compiler

Compiled 38 to 28 computations (26.3% saved)

soundness16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 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

Compiler

Compiled 22 to 16 computations (27.3% saved)

end40.0ms (0.6%)

Compiler: Compiled 34 to 24 computations (29.4% saved)