Details

analyze3.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.8s (33.1%)

Results

1.2s	2067×	body	1024	valid
963.0ms	4936×	body	256	valid
318.0ms	241×	body	2048	valid
261.0ms	1012×	body	512	valid

preprocess36.0ms (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)

simplify37.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 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)

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

27.4b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	27.4b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize14.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.8b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series4.0ms (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))

rewrite88.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

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

Outputs

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

simplify160.0ms (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))))

eval21.0ms (0.3%)

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

prune134.0ms (1.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	37	13	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	14	51

Error

0.1b

Counts

51 → 14

Alt Table

Click to see full alt table

Status	Error	Program
	28.2b	(pow.f64 (pow.f64 (-.f64 (log1p.f64 N) (log.f64 N)) 3) 1/3)
✓	27.4b	(-.f64 (log1p.f64 N) (log.f64 N))
▶	28.0b	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
▶	31.3b	(neg.f64 (log.f64 N))
	28.0b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 N) (log.f64 N))))
	32.9b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
▶	27.2b	(log.f64 (/.f64 (+.f64 N 1) N))
	33.7b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
	30.2b	(-.f64 N (log.f64 N))
	28.6b	(+.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)))
	27.5b	(/.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)))))
	33.4b	(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 -1/4 N) 1/3))))
▶	32.9b	(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (.f64 1/2 (/.f64 1 (pow.f64 N 2))))
▶	32.6b	(/.f64 1 N)

Compiler

Compiled 326 to 226 computations (30.7% saved)

localize19.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 N 1) N)
✓	3.8b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 17 to 11 computations (35.3% saved)

series5.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite84.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 60

Calls

Call 1

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

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

Outputs

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

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

simplify55.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

localize6.0ms (0.1%)

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

localize10.0ms (0.1%)

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

localize60.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (pow.f64 N 3))
✓	0.2b	(*.f64 1/2 (/.f64 1 (pow.f64 N 2)))
✓	0.3b	(/.f64 1 (pow.f64 N 2))
✓	11.0b	(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (.f64 1/2 (/.f64 1 (pow.f64 N 2))))

Compiler

Compiled 70 to 57 computations (18.6% saved)

series10.0ms (0.1%)

Counts

4 → 20

Calls

12 calls:

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

rewrite166.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

693×	`log-prod_binary64`
689×	`fma-def_binary64`
369×	`fma-neg_binary64`
271×	`expm1-udef_binary64`
271×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	37
1	377	35
2	4849	33

Stop Event

1×	node limit

Counts

4 → 235

Calls

Call 1

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

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

simplify105.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

754×	`fma-neg_binary64`
709×	`distribute-neg-frac_binary64`
536×	`unswap-sqr_binary64`
459×	`associate-/r/_binary64`
332×	`associate-/r*_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	20	185
1	51	185
2	99	185
3	216	185
4	596	185
5	2540	181
6	6094	181

Stop Event

1×	node limit

Counts

255 → 244

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

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))))
(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))))
(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 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 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))

localize27.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (log1p.f64 N))
✓	27.8b	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))

Compiler

Compiled 22 to 6 computations (72.7% saved)

series37.0ms (0.4%)

Counts

2 → 17

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	N	@	inf	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
8.0ms	N	@	-inf	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
5.0ms	N	@	inf	(sqrt.f64 (log1p.f64 N))
3.0ms	N	@	0	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
2.0ms	N	@	-inf	(sqrt.f64 (log1p.f64 N))

rewrite119.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

527×	`pow1_binary64`
506×	`add-sqr-sqrt_binary64`
486×	`add-log-exp_binary64`
485×	`expm1-log1p-u_binary64`
484×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	139	13
2	1631	13

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
(sqrt.f64 (log1p.f64 N))

Outputs

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

simplify135.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

613×	`fma-def_binary64`
509×	`fma-neg_binary64`
452×	`associate-/r*_binary64`
427×	`associate-l_binary64`
381×	`times-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1509
1	414	1258
2	1526	1014
3	7242	1010

Stop Event

1×	node limit

Counts

59 → 75

Calls

Call 1

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

Outputs
(*.f64 -1 (log.f64 N))
(neg.f64 (log.f64 N))
(-.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N))) (.f64 -1 (log.f64 (/.f64 1 N))))
(*.f64 (neg.f64 (log.f64 N)) (-.f64 (pow.f64 (sqrt.f64 -1) 2) -1))
(*.f64 (log.f64 N) 0)
0
(-.f64 (+.f64 (/.f64 1 N) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))) (.f64 -1 (log.f64 (/.f64 1 N))))
(+.f64 (/.f64 1 N) (*.f64 (neg.f64 (log.f64 N)) (-.f64 (pow.f64 (sqrt.f64 -1) 2) -1)))
(+.f64 (/.f64 1 N) (*.f64 (log.f64 N) 0))
(+.f64 (/.f64 1 N) 0)
(-.f64 (+.f64 (.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (pow.f64 N 2))) (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 N 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))) (+.f64 (/.f64 1 N) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))) (.f64 -1 (log.f64 (/.f64 1 N))))
(-.f64 (fma.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))))) 2)) (.f64 N N)) (+.f64 (+.f64 (/.f64 1 N) (.f64 (pow.f64 (sqrt.f64 -1) 2) (neg.f64 (log.f64 N)))) (/.f64 1/4 (.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (neg.f64 (log.f64 N))) (*.f64 N N))))) (neg.f64 (neg.f64 (log.f64 N))))
(+.f64 (-.f64 (/.f64 1/4 (.f64 N (.f64 N (log.f64 N)))) (/.f64 (+.f64 1/2 (pow.f64 (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (/.f64 1/2 (sqrt.f64 -1))) 2)) (.f64 N N))) (+.f64 (/.f64 1 N) (*.f64 (log.f64 N) 0)))
(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/4 (.f64 (log.f64 N) (.f64 N N))) (/.f64 (+.f64 1/2 (pow.f64 (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (/.f64 1/2 (sqrt.f64 -1))) 2)) (.f64 N N))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 N 2) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))) (+.f64 (.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (pow.f64 N 2))) (+.f64 (/.f64 1 N) (+.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N))) (.f64 1/3 (/.f64 1 (pow.f64 N 3))))))) (*.f64 -1 (log.f64 (/.f64 1 N))))
(+.f64 (/.f64 1/4 (.f64 (.f64 (pow.f64 (sqrt.f64 -1) 2) (neg.f64 (log.f64 N))) (.f64 N N))) (-.f64 (fma.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))))) 2)) (.f64 N N)) (+.f64 (/.f64 1 N) (fma.f64 (pow.f64 (sqrt.f64 -1) 2) (neg.f64 (log.f64 N)) (/.f64 1/3 (pow.f64 N 3))))) (neg.f64 (neg.f64 (log.f64 N)))))
(+.f64 (-.f64 (+.f64 (/.f64 1 N) (+.f64 (log.f64 N) (/.f64 1/3 (pow.f64 N 3)))) (/.f64 (+.f64 1/2 (pow.f64 (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (/.f64 1/2 (sqrt.f64 -1))) 2)) (.f64 N N))) (-.f64 (/.f64 1/4 (.f64 N (.f64 N (log.f64 N)))) (log.f64 N)))
(+.f64 (+.f64 (/.f64 1 N) (-.f64 (/.f64 1/4 (.f64 (log.f64 N) (.f64 N N))) (/.f64 (+.f64 1/2 (pow.f64 (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (/.f64 1/2 (sqrt.f64 -1))) 2)) (.f64 N N)))) (/.f64 1/3 (pow.f64 N 3)))
(/.f64 1 N)
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(fma.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 (log.f64 N))) (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (+.f64 (/.f64 (/.f64 1/2 N) (sqrt.f64 -1)) (/.f64 (fma.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (/.f64 1/2 (sqrt.f64 -1))) 2) -1/2 -1/4) (.f64 N (.f64 N (sqrt.f64 -1)))))))
(+.f64 (.f64 1/2 (.f64 (/.f64 (-.f64 1/3 (.f64 -1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 (sqrt.f64 -1) 2) (log.f64 (/.f64 1 N)))))) (.f64 (pow.f64 N 3) (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) (+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) 2)) (.f64 (pow.f64 N 2) (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))) (+.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 (log.f64 (/.f64 1 N)))) (.f64 1/2 (.f64 (/.f64 1 (.f64 N (sqrt.f64 -1))) (sqrt.f64 (/.f64 1 (log.f64 (/.f64 1 N)))))))))
(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))) (/.f64 (+.f64 1/3 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))))) 2)) (.f64 (pow.f64 (sqrt.f64 -1) 2) (neg.f64 (log.f64 N)))))) (.f64 (sqrt.f64 -1) (pow.f64 N 3)))) (fma.f64 -1/2 (.f64 (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))) (/.f64 (+.f64 1/2 (pow.f64 (.f64 1/2 (.f64 (/.f64 1 (sqrt.f64 -1)) (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))))) 2)) (.f64 (sqrt.f64 -1) (.f64 N N)))) (fma.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 (log.f64 N))) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (neg.f64 (log.f64 N)))) (/.f64 1 (.f64 N (sqrt.f64 -1))))))))
(+.f64 (fma.f64 1/2 (/.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (.f64 N (sqrt.f64 -1))) (.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 (log.f64 N))))) (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (+.f64 (.f64 1/2 (/.f64 (-.f64 1/3 (/.f64 (+.f64 -1/4 (.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (/.f64 1/2 (sqrt.f64 -1))) 2) -1/2)) (log.f64 N))) (.f64 (sqrt.f64 -1) (pow.f64 N 3)))) (.f64 -1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (/.f64 1/2 (sqrt.f64 -1))) 2)) (.f64 N (*.f64 N (sqrt.f64 -1))))))))
(+.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 (neg.f64 (log.f64 N)))) (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (+.f64 (fma.f64 1/2 (/.f64 (fma.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (/.f64 1/2 (sqrt.f64 -1))) 2)) (log.f64 N)) 1/3) (.f64 (sqrt.f64 -1) (pow.f64 N 3))) (/.f64 (fma.f64 (pow.f64 (.f64 (sqrt.f64 (/.f64 -1 (log.f64 N))) (/.f64 1/2 (sqrt.f64 -1))) 2) -1/2 -1/4) (.f64 N (*.f64 N (sqrt.f64 -1))))) (/.f64 (/.f64 1/2 N) (sqrt.f64 -1)))))
(sqrt.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))
(sqrt.f64 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N)))))
(sqrt.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))
(+.f64 (.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (sqrt.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))
(fma.f64 1/2 (*.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))))) (sqrt.f64 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))))
(fma.f64 1/2 (/.f64 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) N) (sqrt.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))))
(+.f64 (.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (pow.f64 N 2)) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (sqrt.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))))
(fma.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))))) (fma.f64 -1/2 (/.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N)))))) (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))))) 2))) (.f64 N N)) (sqrt.f64 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N)))))))
(+.f64 (sqrt.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) (.f64 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) (+.f64 (/.f64 1/2 N) (.f64 -1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))))) 2)) (.f64 N N))))))
(fma.f64 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) (+.f64 (.f64 -1/2 (/.f64 (fma.f64 1/4 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/2) (.f64 N N))) (/.f64 1/2 N)) (sqrt.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))))
(+.f64 (.f64 1/2 (.f64 (/.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) 1/3) (pow.f64 N 3)) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (+.f64 (.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (+.f64 (.f64 -1/2 (.f64 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (pow.f64 N 2)) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (sqrt.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))))
(fma.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N)))))) (/.f64 (fma.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))) 1/3) (pow.f64 N 3))) (fma.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))))) (fma.f64 -1/2 (/.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N)))))) (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))))) 2))) (.f64 N N)) (sqrt.f64 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 N))))))))
(+.f64 (fma.f64 -1/2 (.f64 (/.f64 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) N) (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))))) 2)) N)) (sqrt.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) (.f64 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) (+.f64 (.f64 1/2 (/.f64 (fma.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (*.f64 -1/2 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))))) 2)) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/3) (pow.f64 N 3))) (/.f64 1/2 N))))
(+.f64 (sqrt.f64 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) (.f64 (sqrt.f64 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N))))) (+.f64 (fma.f64 1/2 (/.f64 (fma.f64 1/2 (/.f64 (fma.f64 1/4 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/2) (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/3) (pow.f64 N 3)) (/.f64 1/2 N)) (.f64 -1/2 (/.f64 (fma.f64 1/4 (/.f64 1 (-.f64 (log.f64 -1) (log.f64 (/.f64 -1 N)))) 1/2) (*.f64 N N))))))

eval790.0ms (9.5%)

Compiler: Compiled 9992 to 7395 computations (26% saved)

prune116.0ms (1.4%)

Pruning

16 alts after pruning (12 fresh and 4 done)

	Pruned	Kept	Total
New	424	8	432
Fresh	4	4	8
Picked	0	1	1
Done	2	3	5
Total	430	16	446

Error

0.0b

Counts

446 → 16

Alt Table

Click to see full alt table

Status	Error	Program
	28.2b	(pow.f64 (pow.f64 (-.f64 (log1p.f64 N) (log.f64 N)) 3) 1/3)
✓	27.4b	(-.f64 (log1p.f64 N) (log.f64 N))
✓	28.0b	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
▶	47.6b	(/.f64 (-.f64 (.f64 (-.f64 (pow.f64 N -2) (.f64 (pow.f64 N -6) 1/9)) (.f64 N N)) (.f64 (+.f64 (/.f64 1 N) (.f64 -1/3 (pow.f64 N -3))) 1/2)) (.f64 (+.f64 (/.f64 1 N) (.f64 -1/3 (pow.f64 N -3))) (.f64 N N)))
✓	31.3b	(neg.f64 (log.f64 N))
	46.4b	(fma.f64 (-.f64 (pow.f64 N -2) (.f64 (pow.f64 N -6) 1/9)) (/.f64 1 (+.f64 (/.f64 1 N) (.f64 -1/3 (pow.f64 N -3)))) (*.f64 (pow.f64 N -2) -1/2))
	32.9b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
	32.9b	(-.f64 (+.f64 (/.f64 1 N) (*.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (/.f64 (/.f64 1/2 N) N))
✓	32.6b	(/.f64 1 N)
▶	33.4b	(+.f64 (+.f64 (/.f64 1 N) (/.f64 -1/2 (.f64 N N))) (.f64 (/.f64 1 (pow.f64 N 3)) (-.f64 1/3 (/.f64 1/4 N))))
▶	30.2b	(-.f64 N (log.f64 N))
	28.6b	(+.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)))
	61.4b	0
	27.4b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N))))
▶	33.7b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
▶	27.2b	(log.f64 (+.f64 1 (/.f64 1 N)))

Compiler

Compiled 411 to 302 computations (26.5% saved)

localize14.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.8b	(log.f64 (+.f64 1 (/.f64 1 N)))

Compiler

Compiled 17 to 13 computations (23.5% saved)

series4.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	N	@	inf	(log.f64 (+.f64 1 (/.f64 1 N)))
1.0ms	N	@	-inf	(log.f64 (+.f64 1 (/.f64 1 N)))
1.0ms	N	@	0	(log.f64 (+.f64 1 (/.f64 1 N)))

rewrite58.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

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

Outputs

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

simplify58.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

32 → 35

Calls

Call 1

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

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

localize21.0ms (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))
✓	0.1b	(/.f64 (/.f64 1/2 N) N)

Compiler

Compiled 24 to 16 computations (33.3% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite139.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 294

Calls

Call 1

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

Outputs

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((#(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 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(/.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))))))

simplify56.0ms (0.7%)

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))

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 8 to 3 computations (62.5% saved)

series8.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite49.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs

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

simplify169.0ms (2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

47 → 42

Calls

Call 1

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

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

localize31.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1/3 (/.f64 1/4 N))
	0.1b	(/.f64 1 (pow.f64 N 3))
✓	0.1b	(*.f64 (/.f64 1 (pow.f64 N 3)) (-.f64 1/3 (/.f64 1/4 N)))
✓	0.3b	(/.f64 -1/2 (*.f64 N N))

Compiler

Compiled 75 to 52 computations (30.7% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite80.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

599×	`log-prod_binary64`
351×	`pow2_binary64`
243×	`pow1/3_binary64`
243×	`expm1-udef_binary64`
243×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	319	27
2	3821	27

Stop Event

1×	node limit

Counts

3 → 126

Calls

Call 1

Inputs
(/.f64 -1/2 (*.f64 N N))
(*.f64 (/.f64 1 (pow.f64 N 3)) (-.f64 1/3 (/.f64 1/4 N)))
(-.f64 1/3 (/.f64 1/4 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 (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 (cbrt.f64 (*.f64 -1/2 (pow.f64 N -2))) (cbrt.f64 (/.f64 1/4 (pow.f64 N 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1/4 (pow.f64 N 4))) (cbrt.f64 (*.f64 -1/2 (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 N -2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (/.f64 1 (*.f64 N (neg.f64 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 (/.f64 -1/2 N) (/.f64 1 N))))) (#(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 (/.f64 1/4 (pow.f64 N 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 -1/2) N) 6) 1/3)))) (#(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 (*.f64 N N) -2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (*.f64 (*.f64 N N) -2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/4 (pow.f64 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 (pow.f64 (/.f64 (sqrt.f64 -1/2) 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 0 (*.f64 (pow.f64 N -3) (+.f64 1/3 (/.f64 -1/4 N))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/3 (pow.f64 N -3)) (*.f64 (/.f64 -1/4 N) (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 N -3) 1/3) (*.f64 (pow.f64 N -3) (/.f64 -1/4 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 N -3)) (+.f64 1/3 (/.f64 -1/4 N)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 N -3)) (+.f64 1/3 (/.f64 -1/4 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 N -3)) (+.f64 1/3 (/.f64 -1/4 N))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 N -3)) (+.f64 1/3 (/.f64 -1/4 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 N -3) (+.f64 1/3 (/.f64 -1/4 N))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 (/.f64 1/4 N) (pow.f64 N 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 N 3) (+.f64 1/3 (/.f64 -1/4 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/3 (/.f64 -1/4 N)) (pow.f64 N 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 1/3 (/.f64 -1/4 N))) 2) (/.f64 (pow.f64 N 3) (cbrt.f64 (+.f64 1/3 (/.f64 -1/4 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 1/3 (/.f64 -1/4 N))) (/.f64 (pow.f64 N 3) (sqrt.f64 (+.f64 1/3 (/.f64 -1/4 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/27 (*.f64 1/64 (pow.f64 N -3))) (*.f64 (pow.f64 N 3) (fma.f64 (/.f64 1/4 N) (+.f64 1/3 (/.f64 1/4 N)) 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/9 (*.f64 1/16 (pow.f64 N -2))) (*.f64 (pow.f64 N 3) (+.f64 1/3 (/.f64 1/4 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/3 (/.f64 -1/4 N))) (neg.f64 (pow.f64 N 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (-.f64 1/27 (*.f64 1/64 (pow.f64 N -3)))) (*.f64 (neg.f64 (pow.f64 N 3)) (fma.f64 (/.f64 1/4 N) (+.f64 1/3 (/.f64 1/4 N)) 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (-.f64 1/9 (*.f64 1/16 (pow.f64 N -2)))) (*.f64 (neg.f64 (pow.f64 N 3)) (+.f64 1/3 (/.f64 1/4 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/27 (*.f64 1/64 (pow.f64 N -3))) 1) (*.f64 (fma.f64 (/.f64 1/4 N) (+.f64 1/3 (/.f64 1/4 N)) 1/9) (pow.f64 N 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/9 (*.f64 1/16 (pow.f64 N -2))) 1) (*.f64 (+.f64 1/3 (/.f64 1/4 N)) (pow.f64 N 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/27 (*.f64 1/64 (pow.f64 N -3))) -1) (*.f64 (fma.f64 (/.f64 1/4 N) (+.f64 1/3 (/.f64 1/4 N)) 1/9) (neg.f64 (pow.f64 N 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/9 (*.f64 1/16 (pow.f64 N -2))) -1) (*.f64 (+.f64 1/3 (/.f64 1/4 N)) (neg.f64 (pow.f64 N 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 1/3 (/.f64 -1/4 N)) (*.f64 N N)) N)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 1/3 (/.f64 -1/4 N)) N) (*.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 1/3 (/.f64 -1/4 N)) (pow.f64 N 3/2)) (pow.f64 N 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 1/3 (/.f64 -1/4 N)) 1) (pow.f64 N 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (+.f64 1/3 (/.f64 -1/4 N))) (neg.f64 (pow.f64 N 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/27 (*.f64 1/64 (pow.f64 N -3))) (pow.f64 N -3)) (fma.f64 (/.f64 1/4 N) (+.f64 1/3 (/.f64 1/4 N)) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/9 (*.f64 1/16 (pow.f64 N -2))) (pow.f64 N -3)) (+.f64 1/3 (/.f64 1/4 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 N -3) (-.f64 1/27 (*.f64 1/64 (pow.f64 N -3)))) (fma.f64 (/.f64 1/4 N) (+.f64 1/3 (/.f64 1/4 N)) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 N -3) (-.f64 1/9 (*.f64 1/16 (pow.f64 N -2)))) (+.f64 1/3 (/.f64 1/4 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1/3 (/.f64 -1/4 N)) -1) (neg.f64 (pow.f64 N 3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 N -3) (+.f64 1/3 (/.f64 -1/4 N))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (cbrt.f64 (+.f64 1/3 (/.f64 -1/4 N))) N) 6) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (cbrt.f64 (+.f64 1/3 (/.f64 -1/4 N))) N) 9) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 (+.f64 1/3 (/.f64 -1/4 N))) N) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 N -3/2) (sqrt.f64 (+.f64 1/3 (/.f64 -1/4 N)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (+.f64 1/3 (/.f64 -1/4 N)) 3) (pow.f64 N 9)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 N -9) (pow.f64 (+.f64 1/3 (/.f64 -1/4 N)) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (+.f64 1/3 (/.f64 -1/4 N)) 3) (pow.f64 N -9)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 N 3) (+.f64 1/3 (/.f64 -1/4 N))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (cbrt.f64 (+.f64 1/3 (/.f64 -1/4 N))) N) 6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 N -3)) (+.f64 1/3 (/.f64 -1/4 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 N -3) (+.f64 1/3 (/.f64 -1/4 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (cbrt.f64 (+.f64 1/3 (/.f64 -1/4 N))) N) 9))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 1/3 (/.f64 -1/4 N)) 3) (pow.f64 N 9)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 N -9) (pow.f64 (+.f64 1/3 (/.f64 -1/4 N)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (+.f64 1/3 (/.f64 -1/4 N)) 3) (pow.f64 N -9)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (pow.f64 N -3) (+.f64 1/3 (/.f64 -1/4 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (pow.f64 N -3) (+.f64 1/3 (/.f64 -1/4 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 -3 (log.f64 N) (log.f64 (+.f64 1/3 (/.f64 -1/4 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 -3 (log.f64 N) (log.f64 (+.f64 1/3 (/.f64 -1/4 N)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N -3) 1/3 (*.f64 (pow.f64 N -3) (/.f64 -1/4 N)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/3 (pow.f64 N -3) (*.f64 (/.f64 -1/4 N) (pow.f64 N -3)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/3 (/.f64 -1/4 N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/3 (*.f64 (/.f64 -1/4 N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 1/3 (/.f64 -1/4 N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 -1/4 N) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 1/3 (/.f64 -1/4 N)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (+.f64 1/3 (/.f64 -1/4 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 1/3 (/.f64 -1/4 N))))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 1/3 (/.f64 -1/4 N))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 1/3 (/.f64 -1/4 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/3 (/.f64 -1/4 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 1/3 (/.f64 -1/4 N))) (pow.f64 (cbrt.f64 (+.f64 1/3 (/.f64 -1/4 N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 1/3 (/.f64 -1/4 N))) 2) (cbrt.f64 (+.f64 1/3 (/.f64 -1/4 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 1/3 (/.f64 -1/4 N))) (sqrt.f64 (+.f64 1/3 (/.f64 -1/4 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/27 (*.f64 1/64 (pow.f64 N -3))) (/.f64 1 (fma.f64 (/.f64 1/4 N) (+.f64 1/3 (/.f64 1/4 N)) 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1/9 (*.f64 1/16 (pow.f64 N -2))) (/.f64 1 (+.f64 1/3 (/.f64 1/4 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (/.f64 1/4 N) (+.f64 1/3 (/.f64 1/4 N)) 1/9) (-.f64 1/27 (*.f64 1/64 (pow.f64 N -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1/3 (/.f64 1/4 N)) (-.f64 1/9 (*.f64 1/16 (pow.f64 N -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/27 (*.f64 1/64 (pow.f64 N -3))) (fma.f64 (/.f64 1/4 N) (+.f64 1/3 (/.f64 1/4 N)) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/9 (*.f64 1/16 (pow.f64 N -2))) (+.f64 1/3 (/.f64 1/4 N)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/27 (*.f64 1/64 (pow.f64 N -3)))) (neg.f64 (fma.f64 (/.f64 1/4 N) (+.f64 1/3 (/.f64 1/4 N)) 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/9 (*.f64 1/16 (pow.f64 N -2)))) (neg.f64 (+.f64 1/3 (/.f64 1/4 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/27 (pow.f64 (/.f64 -1/4 N) 3)) (+.f64 1/9 (-.f64 (pow.f64 (/.f64 -1/4 N) 2) (*.f64 1/3 (/.f64 -1/4 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/9 (pow.f64 (/.f64 -1/4 N) 2)) (-.f64 1/3 (/.f64 -1/4 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/3 (/.f64 -1/4 N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/3 (/.f64 -1/4 N)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/3 (/.f64 -1/4 N)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1/3 (/.f64 -1/4 N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/3 (/.f64 -1/4 N))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (/.f64 1/4 N) (+.f64 1/3 (/.f64 1/4 N)) 1/9) (-.f64 1/27 (*.f64 1/64 (pow.f64 N -3)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 1/3 (/.f64 1/4 N)) (-.f64 1/9 (*.f64 1/16 (pow.f64 N -2)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/3 (/.f64 -1/4 N)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1/3 (/.f64 -1/4 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1/3 (/.f64 -1/4 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/3 (/.f64 -1/4 N)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/3 (/.f64 -1/4 N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/3 (/.f64 -1/4 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 1/3 (/.f64 -1/4 N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 1/3 (/.f64 -1/4 N))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 -1/4 N) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/4 (neg.f64 (/.f64 1 N)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 1/16 (pow.f64 N -2))) (neg.f64 (cbrt.f64 (/.f64 1/4 N))) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1/2 (sqrt.f64 N)) (neg.f64 (/.f64 1/2 (sqrt.f64 N))) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (/.f64 1/4 N) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/4 (/.f64 1 N) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 -1/4 N)) 2) (cbrt.f64 (/.f64 -1/4 N)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 -1/4 N)) (sqrt.f64 (/.f64 -1/4 N)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (cbrt.f64 (*.f64 1/16 (pow.f64 N -2)))) (cbrt.f64 (/.f64 1/4 N)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (/.f64 1/2 (sqrt.f64 N))) (/.f64 1/2 (sqrt.f64 N)) 1/3)))))

simplify61.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

932×	`fma-def_binary64`
558×	`distribute-neg-frac_binary64`
378×	`associate-/l/_binary64`
354×	`associate-l_binary64`
349×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	318
1	57	318
2	112	318
3	248	318
4	991	318
5	4289	318
6	6070	318

Stop Event

1×	node limit

Counts

162 → 135

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

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

localize58.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	14.0b	(-.f64 (pow.f64 N -2) (*.f64 (pow.f64 N -6) 1/9))
✓	21.0b	(-.f64 (.f64 (-.f64 (pow.f64 N -2) (.f64 (pow.f64 N -6) 1/9)) (.f64 N N)) (.f64 (+.f64 (/.f64 1 N) (*.f64 -1/3 (pow.f64 N -3))) 1/2))
✓	29.0b	(.f64 (-.f64 (pow.f64 N -2) (.f64 (pow.f64 N -6) 1/9)) (*.f64 N N))
✓	34.3b	(.f64 (+.f64 (/.f64 1 N) (.f64 -1/3 (pow.f64 N -3))) (*.f64 N N))

Compiler

Compiled 153 to 109 computations (28.8% saved)

series8.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(.f64 (-.f64 (pow.f64 N -2) (.f64 (pow.f64 N -6) 1/9)) (*.f64 N N))
1.0ms	N	@	-inf	(.f64 (-.f64 (pow.f64 N -2) (.f64 (pow.f64 N -6) 1/9)) (*.f64 N N))
1.0ms	N	@	inf	(.f64 (-.f64 (pow.f64 N -2) (.f64 (pow.f64 N -6) 1/9)) (*.f64 N N))
1.0ms	N	@	0	(.f64 (+.f64 (/.f64 1 N) (.f64 -1/3 (pow.f64 N -3))) (*.f64 N N))
1.0ms	N	@	inf	(.f64 (+.f64 (/.f64 1 N) (.f64 -1/3 (pow.f64 N -3))) (*.f64 N N))

rewrite96.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

371×	`expm1-udef_binary64`
371×	`log1p-udef_binary64`
244×	`add-sqr-sqrt_binary64`
233×	`add-log-exp_binary64`
233×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	88
1	509	80
2	6820	80

Stop Event

1×	node limit

Counts

4 → 141

Calls

Call 1

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

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

simplify62.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

924×	`fma-neg_binary64`
637×	`associate-*l/_binary64`
561×	`associate-*r/_binary64`
467×	`associate-/l*_binary64`
467×	`unswap-sqr_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	42	501
1	116	501
2	248	501
3	605	501
4	2412	501
5	7660	493

Stop Event

1×	node limit

Counts

189 → 165

Calls

Call 1

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

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

eval633.0ms (7.6%)

Compiler: Compiled 21514 to 15641 computations (27.3% saved)

prune189.0ms (2.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	701	10	711
Fresh	6	1	7
Picked	1	0	1
Done	6	2	8
Total	714	13	727

Error

Counts

727 → 13

Alt Table

Click to see full alt table

Status	Error	Program
	33.4b	(+.f64 (+.f64 (/.f64 1 N) (/.f64 -1/2 (.f64 N N))) (/.f64 (/.f64 (+.f64 1/3 (/.f64 -1/4 N)) (.f64 N N)) N))
	60.8b	N
	1.3b	(pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 N))) 3)
▶	32.9b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
✓	32.6b	(/.f64 1 N)
▶	33.7b	(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
	47.2b	(/.f64 1 (/.f64 (.f64 N N) (-.f64 N (/.f64 (.f64 N 1/2) N))))
✓	31.3b	(neg.f64 (log.f64 N))
▶	0.0b	(log1p.f64 (/.f64 1 N))
	61.4b	0
▶	17.7b	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))
	33.7b	(*.f64 (/.f64 1 N) (+.f64 1 (/.f64 -1/2 N)))
▶	33.7b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)

Compiler

Compiled 214 to 159 computations (25.7% saved)

localize12.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 10 to 7 computations (30% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	N	@	0	(log1p.f64 (/.f64 1 N))
1.0ms	N	@	-inf	(log1p.f64 (/.f64 1 N))
0.0ms	N	@	inf	(log1p.f64 (/.f64 1 N))

rewrite73.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 27

Calls

Call 1

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

Outputs

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

simplify64.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

39 → 42

Calls

Call 1

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

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

localize17.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 19 to 14 computations (26.3% saved)

series5.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite99.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 62

Calls

Call 1

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

Outputs

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

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

simplify79.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

86 → 71

Calls

Call 1

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

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

localize24.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 28 to 21 computations (25% saved)

series4.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite146.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 75

Calls

Call 1

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

Outputs

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

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

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	270
1	105	270
2	232	268
3	626	261
4	1674	255
5	4149	255
6	7758	255

Stop Event

1×	node limit

Counts

99 → 94

Calls

Call 1

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

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
✓	0.1b	(.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2))
✓	0.3b	(/.f64 1 (*.f64 N N))
✓	0.3b	(/.f64 1/3 N)

Compiler

Compiled 50 to 32 computations (36% saved)

series6.0ms (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	@	0	(/.f64 1/3 N)
0.0ms	N	@	inf	(/.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))

rewrite83.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	274	38
2	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
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(pow.f64 N -2)) (pow.f64 N -1))))))

simplify77.0ms (0.9%)

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))

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (/.f64 1 N))
✓	0.5b	(pow.f64 (log1p.f64 (/.f64 1 N)) 3)
✓	17.6b	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))

Compiler

Compiled 24 to 19 computations (20.8% saved)

series7.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	N	@	0	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))
1.0ms	N	@	0	(pow.f64 (log1p.f64 (/.f64 1 N)) 3)
0.0ms	N	@	inf	(pow.f64 (log1p.f64 (/.f64 1 N)) 3)
0.0ms	N	@	-inf	(pow.f64 (log1p.f64 (/.f64 1 N)) 3)
0.0ms	N	@	inf	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))

rewrite52.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

565×	`pow1_binary64`
533×	`add-log-exp_binary64`
532×	`expm1-log1p-u_binary64`
531×	`log1p-expm1-u_binary64`
519×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	164	15
2	1563	15

Stop Event

1×	node limit

Counts

2 → 38

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))
(pow.f64 (log1p.f64 (/.f64 1 N)) 3)

Outputs

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

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

simplify90.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

643×	`distribute-rgt-in_binary64`
625×	`fma-neg_binary64`
617×	`distribute-lft-in_binary64`
506×	`fma-def_binary64`
319×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	536
1	257	526
2	821	499
3	3591	481

Stop Event

1×	node limit

Counts

62 → 68

Calls

Call 1

Inputs
(*.f64 -1 (log.f64 N))
(+.f64 N (*.f64 -1 (log.f64 N)))
(+.f64 N (+.f64 (.f64 -1 (log.f64 N)) (.f64 -1/2 (pow.f64 N 2))))
(+.f64 N (+.f64 (.f64 -1 (log.f64 N)) (+.f64 (.f64 1/3 (pow.f64 N 3)) (*.f64 -1/2 (pow.f64 N 2)))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
(/.f64 1 N)
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
(*.f64 -1 (pow.f64 (log.f64 N) 3))
(+.f64 (.f64 -1 (pow.f64 (log.f64 N) 3)) (.f64 N (+.f64 (pow.f64 (log.f64 N) 2) (*.f64 2 (pow.f64 (log.f64 N) 2)))))
(+.f64 (.f64 -1 (pow.f64 (log.f64 N) 3)) (+.f64 (.f64 (pow.f64 N 2) (+.f64 (.f64 -1/2 (pow.f64 (log.f64 N) 2)) (+.f64 (.f64 -1 (.f64 (log.f64 N) (+.f64 (log.f64 N) 1))) (.f64 -2 (log.f64 N))))) (.f64 N (+.f64 (pow.f64 (log.f64 N) 2) (.f64 2 (pow.f64 (log.f64 N) 2))))))
(+.f64 (.f64 (pow.f64 N 3) (+.f64 1 (+.f64 (.f64 2 (log.f64 N)) (+.f64 (.f64 -1 (.f64 (log.f64 N) (-.f64 (.f64 -2/3 (log.f64 N)) 1))) (.f64 1/3 (pow.f64 (log.f64 N) 2)))))) (+.f64 (.f64 -1 (pow.f64 (log.f64 N) 3)) (+.f64 (.f64 (pow.f64 N 2) (+.f64 (.f64 -1/2 (pow.f64 (log.f64 N) 2)) (+.f64 (.f64 -1 (.f64 (log.f64 N) (+.f64 (log.f64 N) 1))) (.f64 -2 (log.f64 N))))) (.f64 N (+.f64 (pow.f64 (log.f64 N) 2) (.f64 2 (pow.f64 (log.f64 N) 2)))))))
(/.f64 1 (pow.f64 N 3))
(-.f64 (/.f64 1 (pow.f64 N 3)) (*.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (+.f64 (.f64 3/2 (/.f64 1 (pow.f64 N 4))) (*.f64 15/8 (/.f64 1 (pow.f64 N 6)))))
(/.f64 1 (pow.f64 N 3))
(-.f64 (/.f64 1 (pow.f64 N 3)) (*.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (+.f64 (.f64 3/2 (/.f64 1 (pow.f64 N 4))) (*.f64 15/8 (/.f64 1 (pow.f64 N 6)))))

Outputs
(*.f64 -1 (log.f64 N))
(neg.f64 (log.f64 N))
(+.f64 N (*.f64 -1 (log.f64 N)))
(+.f64 N (neg.f64 (log.f64 N)))
(-.f64 N (log.f64 N))
(+.f64 N (+.f64 (.f64 -1 (log.f64 N)) (.f64 -1/2 (pow.f64 N 2))))
(+.f64 N (fma.f64 -1 (log.f64 N) (.f64 -1/2 (.f64 N N))))
(+.f64 N (-.f64 (.f64 N (.f64 N -1/2)) (log.f64 N)))
(-.f64 (fma.f64 N (*.f64 N -1/2) N) (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 N (-.f64 (.f64 (.f64 N N) (+.f64 (*.f64 N 1/3) -1/2)) (log.f64 N)))
(fma.f64 N (.f64 N (+.f64 -1/2 (.f64 N 1/3))) (-.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 (/.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 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.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 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4)))))
(+.f64 (-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/4 (pow.f64 N 4))) (/.f64 -1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 -1/2 (*.f64 N N)) (/.f64 -1/4 (pow.f64 N 4)))))
(/.f64 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 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.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 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4)))))
(+.f64 (-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (/.f64 1/4 (pow.f64 N 4))) (/.f64 -1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 -1/2 (*.f64 N N)) (/.f64 -1/4 (pow.f64 N 4)))))
(*.f64 -1 (pow.f64 (log.f64 N) 3))
(neg.f64 (pow.f64 (log.f64 N) 3))
(+.f64 (.f64 -1 (pow.f64 (log.f64 N) 3)) (.f64 N (+.f64 (pow.f64 (log.f64 N) 2) (*.f64 2 (pow.f64 (log.f64 N) 2)))))
(fma.f64 -1 (pow.f64 (log.f64 N) 3) (.f64 N (.f64 3 (pow.f64 (log.f64 N) 2))))
(-.f64 (.f64 N (.f64 3 (pow.f64 (log.f64 N) 2))) (pow.f64 (log.f64 N) 3))
(.f64 (pow.f64 (log.f64 N) 2) (-.f64 (.f64 N 3) (log.f64 N)))
(+.f64 (.f64 -1 (pow.f64 (log.f64 N) 3)) (+.f64 (.f64 (pow.f64 N 2) (+.f64 (.f64 -1/2 (pow.f64 (log.f64 N) 2)) (+.f64 (.f64 -1 (.f64 (log.f64 N) (+.f64 (log.f64 N) 1))) (.f64 -2 (log.f64 N))))) (.f64 N (+.f64 (pow.f64 (log.f64 N) 2) (.f64 2 (pow.f64 (log.f64 N) 2))))))
(fma.f64 -1 (pow.f64 (log.f64 N) 3) (fma.f64 (.f64 N N) (fma.f64 -1/2 (pow.f64 (log.f64 N) 2) (fma.f64 -1 (.f64 (log.f64 N) (+.f64 (log.f64 N) 1)) (.f64 (log.f64 N) -2))) (.f64 N (*.f64 3 (pow.f64 (log.f64 N) 2)))))
(-.f64 (fma.f64 N (.f64 3 (pow.f64 (log.f64 N) 2)) (.f64 (.f64 N N) (fma.f64 -1/2 (pow.f64 (log.f64 N) 2) (-.f64 (.f64 (log.f64 N) -2) (+.f64 (log.f64 N) (pow.f64 (log.f64 N) 2)))))) (pow.f64 (log.f64 N) 3))
(fma.f64 N (.f64 N (fma.f64 -1/2 (pow.f64 (log.f64 N) 2) (.f64 (log.f64 N) (-.f64 -2 (+.f64 (log.f64 N) 1))))) (.f64 (pow.f64 (log.f64 N) 2) (-.f64 (.f64 N 3) (log.f64 N))))
(fma.f64 N (.f64 N (fma.f64 (log.f64 N) -2 (-.f64 (.f64 (pow.f64 (log.f64 N) 2) -3/2) (log.f64 N)))) (.f64 (pow.f64 (log.f64 N) 2) (-.f64 (.f64 N 3) (log.f64 N))))
(+.f64 (.f64 (pow.f64 N 3) (+.f64 1 (+.f64 (.f64 2 (log.f64 N)) (+.f64 (.f64 -1 (.f64 (log.f64 N) (-.f64 (.f64 -2/3 (log.f64 N)) 1))) (.f64 1/3 (pow.f64 (log.f64 N) 2)))))) (+.f64 (.f64 -1 (pow.f64 (log.f64 N) 3)) (+.f64 (.f64 (pow.f64 N 2) (+.f64 (.f64 -1/2 (pow.f64 (log.f64 N) 2)) (+.f64 (.f64 -1 (.f64 (log.f64 N) (+.f64 (log.f64 N) 1))) (.f64 -2 (log.f64 N))))) (.f64 N (+.f64 (pow.f64 (log.f64 N) 2) (.f64 2 (pow.f64 (log.f64 N) 2)))))))
(fma.f64 (pow.f64 N 3) (+.f64 1 (fma.f64 2 (log.f64 N) (fma.f64 -1 (.f64 (log.f64 N) (fma.f64 -2/3 (log.f64 N) -1)) (.f64 1/3 (pow.f64 (log.f64 N) 2))))) (fma.f64 -1 (pow.f64 (log.f64 N) 3) (fma.f64 (.f64 N N) (fma.f64 -1/2 (pow.f64 (log.f64 N) 2) (fma.f64 -1 (.f64 (log.f64 N) (+.f64 (log.f64 N) 1)) (.f64 (log.f64 N) -2))) (.f64 N (*.f64 3 (pow.f64 (log.f64 N) 2))))))
(fma.f64 (pow.f64 N 3) (+.f64 1 (fma.f64 (log.f64 N) 2 (fma.f64 (neg.f64 (log.f64 N)) (fma.f64 (log.f64 N) -2/3 -1) (.f64 1/3 (pow.f64 (log.f64 N) 2))))) (-.f64 (fma.f64 N (.f64 3 (pow.f64 (log.f64 N) 2)) (.f64 (.f64 N N) (fma.f64 -1/2 (pow.f64 (log.f64 N) 2) (-.f64 (*.f64 (log.f64 N) -2) (+.f64 (log.f64 N) (pow.f64 (log.f64 N) 2)))))) (pow.f64 (log.f64 N) 3)))
(fma.f64 (pow.f64 N 3) (+.f64 1 (fma.f64 1/3 (pow.f64 (log.f64 N) 2) (.f64 (log.f64 N) (-.f64 2 (fma.f64 (log.f64 N) -2/3 -1))))) (fma.f64 N (.f64 N (fma.f64 -1/2 (pow.f64 (log.f64 N) 2) (.f64 (log.f64 N) (-.f64 -2 (+.f64 (log.f64 N) 1))))) (.f64 (pow.f64 (log.f64 N) 2) (-.f64 (*.f64 N 3) (log.f64 N)))))
(fma.f64 (pow.f64 N 3) (+.f64 1 (.f64 (log.f64 N) (-.f64 (+.f64 (log.f64 N) 1) -2))) (fma.f64 N (.f64 N (fma.f64 (log.f64 N) -2 (-.f64 (.f64 (pow.f64 (log.f64 N) 2) -3/2) (log.f64 N)))) (.f64 (pow.f64 (log.f64 N) 2) (-.f64 (*.f64 N 3) (log.f64 N)))))
(/.f64 1 (pow.f64 N 3))
(-.f64 (/.f64 1 (pow.f64 N 3)) (*.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 3/2 (pow.f64 N 4)))
(+.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 -3/2 (pow.f64 N 4)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 7/4 (pow.f64 N 5))) (/.f64 3/2 (pow.f64 N 4)))
(+.f64 (/.f64 7/4 (pow.f64 N 5)) (+.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 -3/2 (pow.f64 N 4))))
(+.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 7/4 (pow.f64 N 5)) (/.f64 -3/2 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (+.f64 (.f64 3/2 (/.f64 1 (pow.f64 N 4))) (*.f64 15/8 (/.f64 1 (pow.f64 N 6)))))
(+.f64 (/.f64 1 (pow.f64 N 3)) (-.f64 (/.f64 7/4 (pow.f64 N 5)) (+.f64 (/.f64 3/2 (pow.f64 N 4)) (/.f64 15/8 (pow.f64 N 6)))))
(+.f64 (/.f64 7/4 (pow.f64 N 5)) (-.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 3/2 (pow.f64 N 4)) (/.f64 15/8 (pow.f64 N 6)))))
(+.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (+.f64 (/.f64 7/4 (pow.f64 N 5)) (/.f64 -3/2 (pow.f64 N 4))) (/.f64 -15/8 (pow.f64 N 6))))
(/.f64 1 (pow.f64 N 3))
(-.f64 (/.f64 1 (pow.f64 N 3)) (*.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 3/2 (pow.f64 N 4)))
(+.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 -3/2 (pow.f64 N 4)))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (.f64 3/2 (/.f64 1 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 7/4 (pow.f64 N 5))) (/.f64 3/2 (pow.f64 N 4)))
(+.f64 (/.f64 7/4 (pow.f64 N 5)) (+.f64 (/.f64 1 (pow.f64 N 3)) (/.f64 -3/2 (pow.f64 N 4))))
(+.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 7/4 (pow.f64 N 5)) (/.f64 -3/2 (pow.f64 N 4))))
(-.f64 (+.f64 (/.f64 1 (pow.f64 N 3)) (.f64 7/4 (/.f64 1 (pow.f64 N 5)))) (+.f64 (.f64 3/2 (/.f64 1 (pow.f64 N 4))) (*.f64 15/8 (/.f64 1 (pow.f64 N 6)))))
(+.f64 (/.f64 1 (pow.f64 N 3)) (-.f64 (/.f64 7/4 (pow.f64 N 5)) (+.f64 (/.f64 3/2 (pow.f64 N 4)) (/.f64 15/8 (pow.f64 N 6)))))
(+.f64 (/.f64 7/4 (pow.f64 N 5)) (-.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 3/2 (pow.f64 N 4)) (/.f64 15/8 (pow.f64 N 6)))))
(+.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (+.f64 (/.f64 7/4 (pow.f64 N 5)) (/.f64 -3/2 (pow.f64 N 4))) (/.f64 -15/8 (pow.f64 N 6))))

eval245.0ms (2.9%)

Compiler: Compiled 8689 to 6719 computations (22.7% saved)

prune123.0ms (1.5%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	556	2	558
Fresh	2	4	6
Picked	0	1	1
Done	3	3	6
Total	561	10	571

Error

Counts

571 → 10

Alt Table

Click to see full alt table

Status	Error	Program
	33.4b	(+.f64 (+.f64 (/.f64 1 N) (/.f64 -1/2 (.f64 N N))) (/.f64 (/.f64 (+.f64 1/3 (/.f64 -1/4 N)) (.f64 N N)) N))
	60.8b	N
	29.1b	(/.f64 1 (+.f64 N 1/2))
✓	31.3b	(neg.f64 (log.f64 N))
✓	0.0b	(log1p.f64 (/.f64 1 N))
	61.4b	0
✓	17.7b	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))
	32.9b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
	1.3b	(pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 N))) 3)
✓	32.6b	(/.f64 1 N)

Compiler

Compiled 75 to 56 computations (25.3% saved)

regimes47.0ms (0.6%)

Counts

35 → 1

Calls

Call 1

Inputs
N
0
(/.f64 1 N)
(/.f64 1 (+.f64 N 1/2))
(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
(*.f64 (/.f64 1 N) (+.f64 1 (/.f64 -1/2 N)))
(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
(/.f64 1 (/.f64 (.f64 N N) (-.f64 N (/.f64 (.f64 N 1/2) N))))
(+.f64 (/.f64 1 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)))
(+.f64 (+.f64 (/.f64 1 N) (/.f64 -1/2 (.f64 N N))) (/.f64 (/.f64 (+.f64 1/3 (/.f64 -1/4 N)) (.f64 N N)) N))
(neg.f64 (log.f64 N))
(log1p.f64 (/.f64 1 N))
(-.f64 N (log.f64 N))
(-.f64 N (log.f64 N))
(log.f64 (+.f64 1 (/.f64 1 N)))
(log.f64 (/.f64 (+.f64 N 1) N))
(-.f64 (+.f64 (/.f64 1 N) (*.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (/.f64 (/.f64 1/2 N) N))
(+.f64 (+.f64 (/.f64 1 N) (/.f64 -1/2 (.f64 N N))) (.f64 (/.f64 1 (pow.f64 N 3)) (-.f64 1/3 (/.f64 1/4 N))))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 -1/4 N) 1/3))))
(-.f64 (log1p.f64 N) (log.f64 N))
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(pow.f64 (cbrt.f64 (log1p.f64 (/.f64 1 N))) 3)
(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))
(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 N) (log.f64 N))))
(pow.f64 (pow.f64 (-.f64 (log1p.f64 N) (log.f64 N)) 3) 1/3)
(/.f64 (-.f64 (.f64 (-.f64 (pow.f64 N -2) (.f64 (pow.f64 N -6) 1/9)) (.f64 N N)) (.f64 (+.f64 (/.f64 1 N) (.f64 -1/3 (pow.f64 N -3))) 1/2)) (.f64 (+.f64 (/.f64 1 N) (.f64 -1/3 (pow.f64 N -3))) (.f64 N N)))
(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N))))
(fma.f64 (-.f64 (pow.f64 N -2) (.f64 (pow.f64 N -6) 1/9)) (/.f64 1 (+.f64 (/.f64 1 N) (.f64 -1/3 (pow.f64 N -3)))) (*.f64 (pow.f64 N -2) -1/2))
(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
(+.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)))
(/.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)))))

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

Calls

3 calls:

16.0ms	N
12.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
8.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

Results

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

Compiler

Compiled 420 to 273 computations (35% saved)

regimes55.0ms (0.7%)

Counts

14 → 2

Calls

Call 1

Inputs
N
0
(/.f64 1 N)
(/.f64 1 (+.f64 N 1/2))
(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
(*.f64 (/.f64 1 N) (+.f64 1 (/.f64 -1/2 N)))
(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
(/.f64 1 (/.f64 (.f64 N N) (-.f64 N (/.f64 (.f64 N 1/2) N))))
(+.f64 (/.f64 1 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)))
(+.f64 (+.f64 (/.f64 1 N) (/.f64 -1/2 (.f64 N N))) (/.f64 (/.f64 (+.f64 1/3 (/.f64 -1/4 N)) (.f64 N N)) N))
(neg.f64 (log.f64 N))

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

Calls

1 calls:

51.0ms

Results

Error	Segments	Branch
1.4b	2	`N`

Compiler

Compiled 127 to 85 computations (33.1% saved)

bsearch24.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
24.0ms	0.06185657187349748	26.446445485194413

Compiler

Compiled 12 to 9 computations (25% saved)

regimes11.0ms (0.1%)

Counts

13 → 1

Calls

Call 1

Inputs
N
0
(/.f64 1 N)
(/.f64 1 (+.f64 N 1/2))
(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
(*.f64 (/.f64 1 N) (+.f64 1 (/.f64 -1/2 N)))
(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
(/.f64 1 (/.f64 (.f64 N N) (-.f64 N (/.f64 (.f64 N 1/2) N))))
(+.f64 (/.f64 1 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)))
(+.f64 (+.f64 (/.f64 1 N) (/.f64 -1/2 (.f64 N N))) (/.f64 (/.f64 (+.f64 1/3 (/.f64 -1/4 N)) (.f64 N N)) N))

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

Calls

1 calls:

8.0ms

Results

Error	Segments	Branch
29.1b	1	`N`

Compiler

Compiled 124 to 83 computations (33.1% saved)

regimes5.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

Inputs
N
0
(/.f64 1 N)

Outputs
(/.f64 1 N)

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
32.6b	1	`N`

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes4.0ms (0%)

Accuracy

Total -1.3b remaining (-2.1%)

Threshold costs -1.3b (-2.1%)

Counts

2 → 1

Calls

Call 1

Inputs
N
0

Outputs
N

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
60.8b	1	`N`

Compiler

Compiled 5 to 3 computations (40% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	60
1	34	60
2	36	60
3	37	60

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(log1p.f64 (/.f64 1 N))
(if (<=.f64 N 4457235744638393/72057594037927936) (neg.f64 (log.f64 N)) (+.f64 (+.f64 (/.f64 1 N) (/.f64 -1/2 (.f64 N N))) (/.f64 (/.f64 (+.f64 1/3 (/.f64 -1/4 N)) (.f64 N N)) N)))
(/.f64 1 (+.f64 N 1/2))
(/.f64 1 N)
N

Outputs
(log1p.f64 (/.f64 1 N))
(if (<=.f64 N 4457235744638393/72057594037927936) (neg.f64 (log.f64 N)) (+.f64 (+.f64 (/.f64 1 N) (/.f64 -1/2 (.f64 N N))) (/.f64 (/.f64 (+.f64 1/3 (/.f64 -1/4 N)) (.f64 N N)) N)))
(/.f64 1 (+.f64 N 1/2))
(/.f64 1 N)
N

Compiler

Compiled 46 to 32 computations (30.4% saved)

soundness14.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×

saturated

Compiler

Compiled 22 to 16 computations (27.3% saved)

end60.0ms (0.7%)

Compiler: Compiled 42 to 28 computations (33.3% saved)