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)

sample3.3s (55.4%)

Results

1.4s	2050×	body	1024	valid
1.2s	4883×	body	256	valid
465.0ms	1049×	body	512	valid
232.0ms	274×	body	2048	valid

preprocess21.0ms (0.4%)

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)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 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

30.2b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.2b	(-.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
✓	2.5b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite52.0ms (0.9%)

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)))))))

simplify114.0ms (1.9%)

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)

prune37.0ms (0.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	5	51

Error

0.0b

Counts

51 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.7b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
▶	31.2b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
▶	30.0b	(/.f64 1 N)
▶	31.6b	(-.f64 N (log.f64 N))
▶	32.2b	(neg.f64 (log.f64 N))

Compiler

Compiled 78 to 56 computations (28.2% saved)

localize2.0ms (0%)

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

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 24 to 16 computations (33.3% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite110.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 294

Calls

Call 1

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

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

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

simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

318 → 300

Calls

Call 1

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

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

localize19.0ms (0.3%)

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))
✓	0.2b	(/.f64 1 (*.f64 N N))
✓	0.4b	(/.f64 1/3 N)

Compiler

Compiled 50 to 32 computations (36% saved)

series7.0ms (0.1%)

Counts

4 → 36

Calls

12 calls:

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

rewrite97.0ms (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	3773	38

Stop Event

1×	node limit

Counts

4 → 193

Calls

Call 1

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

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

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

229 → 206

Calls

Call 1

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

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

localize5.0ms (0.1%)

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

localize5.0ms (0.1%)

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

eval428.0ms (7.1%)

Compiler: Compiled 12433 to 9240 computations (25.7% saved)

prune68.0ms (1.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	502	4	506
Fresh	0	0	0
Picked	0	1	1
Done	2	2	4
Total	504	7	511

Error

Counts

511 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.0b	(/.f64 1 N)
▶	31.2b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
▶	31.2b	(*.f64 (/.f64 1 N) (+.f64 1 (/.f64 -1/2 N)))
▶	30.7b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
▶	54.0b	(/.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)))
✓	31.6b	(-.f64 N (log.f64 N))
✓	32.2b	(neg.f64 (log.f64 N))

Compiler

Compiled 65 to 44 computations (32.3% saved)

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 24 to 18 computations (25% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite64.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

906×	`pow1_binary64`
849×	`add-log-exp_binary64`
848×	`log1p-expm1-u_binary64`
848×	`expm1-log1p-u_binary64`
833×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	180	10
2	2422	10

Stop Event

1×	node limit

Counts

1 → 45

Calls

Call 1

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

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

simplify46.0ms (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

57 → 50

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))

localize27.0ms (0.4%)

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)
	0.4b	(/.f64 1/3 N)

Compiler

Compiled 45 to 32 computations (28.9% saved)

series3.0ms (0.1%)

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 1/3 N) -1/2) N)
0.0ms	N	@	0	(/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)
0.0ms	N	@	inf	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
0.0ms	N	@	-inf	(/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)

rewrite87.0ms (1.4%)

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

simplify64.0ms (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))

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 14 computations (26.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite54.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	154	10
2	2042	10

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

simplify43.0ms (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

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))

localize23.0ms (0.4%)

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))
	0.4b	(/.f64 1/3 N)
✓	23.0b	(/.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)))

Compiler

Compiled 62 to 30 computations (51.6% saved)

series6.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	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	@	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	@	0	(.f64 (neg.f64 N) (.f64 N N))
1.0ms	N	@	inf	(.f64 (neg.f64 N) (.f64 N N))

rewrite111.0ms (1.8%)

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

simplify69.0ms (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))

eval308.0ms (5.1%)

Compiler: Compiled 16140 to 9902 computations (38.6% saved)

prune88.0ms (1.5%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	633	1	634
Fresh	0	0	0
Picked	1	0	1
Done	1	5	6
Total	635	6	641

Error

Counts

641 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.0b	(/.f64 1 N)
✓	31.2b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
▶	30.7b	(*.f64 (/.f64 1 N) (+.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) 1))
✓	31.2b	(*.f64 (/.f64 1 N) (+.f64 1 (/.f64 -1/2 N)))
✓	31.6b	(-.f64 N (log.f64 N))
✓	32.2b	(neg.f64 (log.f64 N))

Compiler

Compiled 45 to 34 computations (24.4% saved)

localize18.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 45 to 34 computations (24.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

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

0.0ms

-inf

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

0.0ms

inf

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

rewrite71.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

564×	`prod-diff_binary64`
561×	`log-prod_binary64`
309×	`pow2_binary64`
247×	`fma-def_binary64`
236×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	256	16
2	3576	16

Stop Event

1×	node limit

Counts

1 → 79

Calls

Call 1

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

Outputs

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

simplify53.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

770×	`fma-neg_binary64`
705×	`distribute-neg-frac_binary64`
536×	`unswap-sqr_binary64`
454×	`associate-/r/_binary64`
328×	`associate-/r*_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	21	189
1	55	189
2	103	189
3	219	189
4	595	189
5	2544	177
6	6092	177

Stop Event

1×	node limit

Counts

91 → 88

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))))

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

eval68.0ms (1.1%)

Compiler: Compiled 3053 to 2405 computations (21.2% saved)

prune22.0ms (0.4%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	165	6	171

Error

Counts

171 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.0b	(/.f64 1 N)
✓	31.2b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
✓	31.2b	(*.f64 (/.f64 1 N) (+.f64 1 (/.f64 -1/2 N)))
	30.7b	(/.f64 (+.f64 1 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)) N)
✓	31.6b	(-.f64 N (log.f64 N))
✓	32.2b	(neg.f64 (log.f64 N))

Compiler

Compiled 43 to 32 computations (25.6% saved)

regimes25.0ms (0.4%)

Counts

13 → 2

Calls

Call 1

Inputs
(/.f64 1 N)
(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
(*.f64 (/.f64 1 N) (+.f64 1 (/.f64 -1/2 N)))
(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
(/.f64 (+.f64 1 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)) N)
(*.f64 (/.f64 1 N) (+.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) 1))
(+.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))
(-.f64 N (log.f64 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 (log1p.f64 N) (log.f64 N))
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

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

Calls

2 calls:

15.0ms	N
6.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

Results

Error	Segments	Branch
0b	2	`N`
0b	2	`(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))`

Compiler

Compiled 129 to 84 computations (34.9% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.272197837134172e-6	21.177029125165102

Compiler

Compiled 12 to 9 computations (25% saved)

regimes14.0ms (0.2%)

Counts

9 → 2

Calls

Call 1

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

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

Calls

1 calls:

12.0ms

Results

Error	Segments	Branch
0.2b	2	`N`

Compiler

Compiled 86 to 62 computations (27.9% saved)

bsearch24.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
24.0ms	6.352330830085446e-10	305604.4939498656

Compiler

Compiled 12 to 9 computations (25% saved)

regimes9.0ms (0.2%)

Accuracy

Total -1.5b remaining (-5.1%)

Threshold costs -1.5b (-5.1%)

Counts

8 → 1

Calls

Call 1

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

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
30.0b	1	`N`

Compiler

Compiled 83 to 60 computations (27.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	69
1	34	69
2	38	69
3	39	69

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs

(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 5902958103587057/1180591620717411303424) (/.f64 (+.f64 1 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)) N) (-.f64 N (log.f64 N)))

(if (<=.f64 N 1535899351044865/2417851639229258349412352) (neg.f64 (log.f64 N)) (/.f64 (+.f64 1 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)) N))

(/.f64 1 N)

Outputs

(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 5902958103587057/1180591620717411303424) (/.f64 (+.f64 1 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)) N) (-.f64 N (log.f64 N)))

(if (<=.f64 N 1535899351044865/2417851639229258349412352) (neg.f64 (log.f64 N)) (/.f64 (+.f64 1 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)) N))

(/.f64 1 N)

Compiler

Compiled 49 to 35 computations (28.6% saved)

soundness182.0ms (3%)

Algorithm

4×	egg-herbie

Rules

746×	`fma-def_binary64`
746×	`fma-def_binary64`
701×	`associate-l_binary64`
701×	`associate-l_binary64`
458×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit
1×	saturated
1×	node limit
1×	saturated

Compiler

Compiled 244 to 192 computations (21.3% saved)

end34.0ms (0.6%)

Compiler: Compiled 47 to 32 computations (31.9% saved)

Details

analyze3.0ms (0%)

sample3.3s (55.4%)

preprocess21.0ms (0.4%)

simplify12.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize7.0ms (0.1%)

series2.0ms (0%)

rewrite52.0ms (0.9%)

simplify114.0ms (1.9%)

eval12.0ms (0.2%)

prune37.0ms (0.6%)

localize2.0ms (0%)

localize10.0ms (0.2%)

series3.0ms (0%)

rewrite110.0ms (1.8%)

simplify52.0ms (0.9%)

localize19.0ms (0.3%)

series7.0ms (0.1%)

rewrite97.0ms (1.6%)

simplify79.0ms (1.3%)

localize5.0ms (0.1%)

localize5.0ms (0.1%)

eval428.0ms (7.1%)

prune68.0ms (1.1%)

localize10.0ms (0.2%)

series2.0ms (0%)

rewrite64.0ms (1.1%)

simplify46.0ms (0.8%)

localize27.0ms (0.4%)

series3.0ms (0.1%)

rewrite87.0ms (1.4%)

simplify64.0ms (1.1%)

localize10.0ms (0.2%)

series1.0ms (0%)

rewrite54.0ms (0.9%)

simplify43.0ms (0.7%)

localize23.0ms (0.4%)

series6.0ms (0.1%)

rewrite111.0ms (1.8%)

simplify69.0ms (1.1%)

eval308.0ms (5.1%)

prune88.0ms (1.5%)

localize18.0ms (0.3%)

series1.0ms (0%)

rewrite71.0ms (1.2%)

simplify53.0ms (0.9%)

eval68.0ms (1.1%)

prune22.0ms (0.4%)

regimes25.0ms (0.4%)

bsearch0.0ms (0%)

regimes14.0ms (0.2%)

bsearch24.0ms (0.4%)

regimes9.0ms (0.2%)

simplify5.0ms (0.1%)

soundness182.0ms (3%)

end34.0ms (0.6%)

Profiling