Details

analyze3.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.9s (32.6%)

Results

767.0ms	2050×	body	1024	valid
747.0ms	4975×	body	256	valid
247.0ms	996×	body	512	valid
141.0ms	235×	body	2048	valid

Bogosity

preprocess22.0ms (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)

simplify16.0ms (0.3%)

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

29.9b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	29.9b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	3.0b	(-.f64 (log1p.f64 N) (log.f64 N))
✓	3.0b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite49.0ms (0.8%)

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)))))))

simplify40.0ms (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

47 → 50

Calls

Call 1

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

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

eval11.0ms (0.2%)

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

prune17.0ms (0.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

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

Error

0.0b

Counts

51 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.1b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
▶	29.8b	(log.f64 (/.f64 (+.f64 N 1) N))
	31.9b	(-.f64 N (log.f64 N))
▶	32.7b	(neg.f64 (log.f64 N))
	31.0b	(+.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))))
▶	30.5b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
▶	30.3b	(/.f64 1 N)

Compiler

Compiled 136 to 100 computations (26.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 17 to 11 computations (35.3% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite61.0ms (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)))))))

simplify44.0ms (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))

localize3.0ms (0.1%)

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

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 24 to 16 computations (33.3% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite260.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 294

Calls

Call 1

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

Outputs

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simplify52.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

318 → 300

Calls

Call 1

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

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

localize20.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.4b	(/.f64 1/3 N)
	0.1b	(.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2))
	0.0b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
	0.0b	(-.f64 (/.f64 1/3 N) 1/2)
✓	0.0b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
✓	0.1b	(.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2))
✓	0.4b	(/.f64 1/3 N)
✓	0.7b	(/.f64 1 (*.f64 N N))

Compiler

Compiled 50 to 32 computations (36% saved)

series5.0ms (0.1%)

Counts

4 → 36

Calls

12 calls:

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

rewrite84.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 193

Calls

Call 1

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

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

simplify62.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

229 → 206

Calls

Call 1

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

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

localize5.0ms (0.1%)

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

eval545.0ms (9.3%)

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

prune82.0ms (1.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	578	5	583
Fresh	0	2	2
Picked	0	1	1
Done	2	2	4
Total	580	10	590

Error

0.0b

Counts

590 → 10

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.5b	(+.f64 (/.f64 1 N) (/.f64 (+.f64 (/.f64 1/3 N) -1/2) (*.f64 N N)))
▶	31.1b	(/.f64 1 (/.f64 N (+.f64 1 (/.f64 -1/2 N))))
▶	29.8b	(+.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))) (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))))
▶	31.1b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
▶	31.9b	(-.f64 N (log.f64 N))
✓	32.7b	(neg.f64 (log.f64 N))
	31.0b	(+.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))))
	52.8b	(/.f64 (fma.f64 N (neg.f64 N) (.f64 (neg.f64 N) (+.f64 (/.f64 1/3 N) -1/2))) (.f64 (neg.f64 N) (*.f64 N N)))
✓	29.8b	(log.f64 (/.f64 (+.f64 N 1) N))
✓	30.3b	(/.f64 1 N)

Compiler

Compiled 205 to 145 computations (29.3% saved)

localize21.0ms (0.4%)

Local error

Found 6 expressions with local error:

New	Error	Program
	2.9b	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
	0.1b	(sqrt.f64 (/.f64 (+.f64 N 1) N))
	0.0b	(/.f64 (+.f64 N 1) N)
	0.0b	(/.f64 (+.f64 N 1) N)
✓	0.1b	(sqrt.f64 (/.f64 (+.f64 N 1) N))
✓	2.9b	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))

Compiler

Compiled 39 to 27 computations (30.8% saved)

series6.0ms (0.1%)

Counts

2 → 16

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	N	@	-inf	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
2.0ms	N	@	0	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
1.0ms	N	@	inf	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
0.0ms	N	@	0	(sqrt.f64 (/.f64 (+.f64 N 1) N))
0.0ms	N	@	-inf	(sqrt.f64 (/.f64 (+.f64 N 1) N))

rewrite61.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 53

Calls

Call 1

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

Outputs

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

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

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

69 → 83

Calls

Call 1

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

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

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 19 to 14 computations (26.3% saved)

series3.0ms (0%)

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

rewrite60.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 62

Calls

Call 1

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

Outputs

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

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

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

86 → 71

Calls

Call 1

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

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

localize12.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite63.0ms (1.1%)

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)))))))

simplify67.0ms (1.1%)

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)))

localize19.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.7b	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) (*.f64 N N))
	0.4b	(/.f64 1/3 N)
	0.0b	(+.f64 (/.f64 1 N) (/.f64 (+.f64 (/.f64 1/3 N) -1/2) (*.f64 N N)))
	0.0b	(+.f64 (/.f64 1/3 N) -1/2)
✓	0.0b	(+.f64 (/.f64 1/3 N) -1/2)
✓	0.0b	(+.f64 (/.f64 1 N) (/.f64 (+.f64 (/.f64 1/3 N) -1/2) (*.f64 N N)))
	0.4b	(/.f64 1/3 N)
✓	0.7b	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) (*.f64 N N))

Compiler

Compiled 41 to 26 computations (36.6% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite84.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

560×	`log-prod_binary64`
407×	`fma-def_binary64`
321×	`pow2_binary64`
267×	`log-div_binary64`
258×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	258	37
2	3843	37

Stop Event

1×	node limit

Counts

3 → 163

Calls

Call 1

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

Outputs

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

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

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

792×	`distribute-neg-frac_binary64`
536×	`unswap-sqr_binary64`
485×	`fma-def_binary64`
333×	`associate-/r*_binary64`
303×	`div-sub_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	26	423
1	62	423
2	112	423
3	232	423
4	656	411
5	3009	375
6	6603	375

Stop Event

1×	node limit

Counts

199 → 178

Calls

Call 1

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

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

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite44.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs

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

simplify156.0ms (2.7%)

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))

eval248.0ms (4.2%)

Compiler: Compiled 11932 to 8569 computations (28.2% saved)

prune99.0ms (1.7%)

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	686	3	689
Fresh	1	1	2
Picked	0	1	1
Done	2	5	7
Total	689	10	699

Error

0.0b

Counts

699 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	32.7b	(neg.f64 (log.f64 N))
▶	26.8b	(/.f64 1 (+.f64 N 1/2))
✓	29.8b	(+.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))) (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))))
✓	30.5b	(+.f64 (/.f64 1 N) (/.f64 (+.f64 (/.f64 1/3 N) -1/2) (*.f64 N N)))
▶	31.0b	(+.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))))
▶	46.0b	(/.f64 (+.f64 N (.f64 N (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N))) (.f64 N N))
✓	31.9b	(-.f64 N (log.f64 N))
	61.1b	N
✓	29.8b	(log.f64 (/.f64 (+.f64 N 1) N))
✓	30.3b	(/.f64 1 N)

Compiler

Compiled 96 to 69 computations (28.1% saved)

localize24.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.4b	(/.f64 1/3 N)
	0.1b	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
	0.0b	(+.f64 (/.f64 1/3 N) -1/2)
	0.0b	(+.f64 N (*.f64 N (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)))
✓	0.1b	(/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)
	0.4b	(/.f64 1/3 N)
✓	13.4b	(*.f64 N (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N))
✓	15.5b	(/.f64 (+.f64 N (.f64 N (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N))) (.f64 N N))

Compiler

Compiled 57 to 36 computations (36.8% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite77.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

661×	`log-prod_binary64`
387×	`fma-def_binary64`
347×	`pow2_binary64`
260×	`log-div_binary64`
240×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	45
1	263	43
2	3949	43

Stop Event

1×	node limit

Counts

3 → 103

Calls

Call 1

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

Outputs

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

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

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

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

619×	`distribute-neg-frac_binary64`
536×	`unswap-sqr_binary64`
405×	`div-sub_binary64`
353×	`fma-neg_binary64`
347×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	30	390
1	74	390
2	133	390
3	266	390
4	796	378
5	3763	369
6	7276	369

Stop Event

1×	node limit

Counts

139 → 121

Calls

Call 1

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

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

localize35.0ms (0.6%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 -1/4 N) 1/3))
	0.0b	(+.f64 (/.f64 -1/4 N) 1/3)
	0.0b	(+.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))))
	0.0b	(+.f64 (/.f64 -1/2 (.f64 N N)) (.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 -1/4 N) 1/3)))
✓	0.0b	(+.f64 (/.f64 -1/4 N) 1/3)
✓	0.1b	(*.f64 (/.f64 1 (pow.f64 N 3)) (+.f64 (/.f64 -1/4 N) 1/3))
✓	0.1b	(/.f64 1 (pow.f64 N 3))
✓	0.7b	(/.f64 -1/2 (*.f64 N N))

Compiler

Compiled 83 to 59 computations (28.9% saved)

series5.0ms (0.1%)

Counts

4 → 36

Calls

12 calls:

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

rewrite81.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

618×	`log-prod_binary64`
360×	`pow2_binary64`
303×	`prod-diff_binary64`
250×	`pow1/3_binary64`
249×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	31
1	324	31
2	4048	31

Stop Event

1×	node limit

Counts

4 → 177

Calls

Call 1

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

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 (/.f64 (sqrt.f64 -1/2) N) (/.f64 (sqrt.f64 -1/2) N))))) (#(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 (pow.f64 N -2) -1/2)))) (#(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 (pow.f64 (.f64 -1/2 (pow.f64 N -2)) 3) 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 -1/2 (pow.f64 N -2)) 3))))) (#(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 (pow.f64 N -3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (pow.f64 N -3))) 2)) (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 (pow.f64 N -3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 N -6)) (/.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 N -2) (/.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 N) (cbrt.f64 (pow.f64 N -6)))))) (#(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 (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 pow.f64 N -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 N 3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 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 pow.f64 (/.f64 1 N) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (sqrt.f64 N) -3) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (pow.f64 N 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 N -6))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 N -3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 N -3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 -3 (log.f64 N)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 N) -3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 N)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 -3 (log.f64 N)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (pow.f64 N -3) (+.f64 (/.f64 -1/4 N) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 -1/4 (pow.f64 N 4)) (.f64 (pow.f64 N -3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 N -3) 1/3) (/.f64 -1/4 (pow.f64 N 4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 -1/4 (pow.f64 N 4)) 1) (.f64 (.f64 (pow.f64 N -3) 1/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 N -3)) (+.f64 (/.f64 -1/4 N) 1/3))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (pow.f64 N -3)) (+.f64 (/.f64 -1/4 N) 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 N -3)) (+.f64 (/.f64 -1/4 N) 1/3)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (pow.f64 N -3)) (+.f64 (/.f64 -1/4 N) 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 N -3) (+.f64 (/.f64 -1/4 N) 1/3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (pow.f64 N 3) (+.f64 (/.f64 -1/4 N) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 -1/4 N) 1/3) (pow.f64 N 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 -1/4 N) 1/3)) 2) (/.f64 (pow.f64 N 3) (cbrt.f64 (+.f64 (/.f64 -1/4 N) 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (/.f64 -1/4 N) 1/3)) (/.f64 (pow.f64 N 3) (sqrt.f64 (+.f64 (/.f64 -1/4 N) 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 -1/64 (pow.f64 N -3) 1/27) (.f64 (pow.f64 N 3) (+.f64 (/.f64 1/16 (.f64 N N)) (-.f64 1/9 (/.f64 -1/12 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 1/16 (.f64 N N)) -1/9) (.f64 (pow.f64 N 3) (+.f64 (/.f64 -1/4 N) -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (/.f64 -1/4 N) 1/3)) (neg.f64 (pow.f64 N 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (fma.f64 -1/64 (pow.f64 N -3) 1/27)) (.f64 (neg.f64 (pow.f64 N 3)) (+.f64 (/.f64 1/16 (.f64 N N)) (-.f64 1/9 (/.f64 -1/12 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (+.f64 (/.f64 1/16 (.f64 N N)) -1/9)) (.f64 (neg.f64 (pow.f64 N 3)) (+.f64 (/.f64 -1/4 N) -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 -1/64 (pow.f64 N -3) 1/27) 1) (.f64 (+.f64 (/.f64 1/16 (.f64 N N)) (-.f64 1/9 (/.f64 -1/12 N))) (pow.f64 N 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (/.f64 1/16 (.f64 N N)) -1/9) 1) (.f64 (+.f64 (/.f64 -1/4 N) -1/3) (pow.f64 N 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 -1/64 (pow.f64 N -3) 1/27) -1) (.f64 (+.f64 (/.f64 1/16 (.f64 N N)) (-.f64 1/9 (/.f64 -1/12 N))) (neg.f64 (pow.f64 N 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (/.f64 1/16 (.f64 N N)) -1/9) -1) (.f64 (+.f64 (/.f64 -1/4 N) -1/3) (neg.f64 (pow.f64 N 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 (/.f64 -1/4 N) 1/3) (.f64 N N)) N)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 (/.f64 -1/4 N) 1/3) N) (.f64 N N))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 (/.f64 -1/4 N) 1/3) (pow.f64 N 3/2)) (pow.f64 N 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (/.f64 -1/4 (pow.f64 N 4)) 3) (pow.f64 (.f64 (pow.f64 N -3) 1/3) 3)) (+.f64 (pow.f64 (/.f64 -1/4 (pow.f64 N 4)) 2) (-.f64 (pow.f64 (.f64 (pow.f64 N -3) 1/3) 2) (.f64 (/.f64 -1/4 (pow.f64 N 4)) (.f64 (pow.f64 N -3) 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (/.f64 -1/4 (pow.f64 N 4)) 2) (pow.f64 (.f64 (pow.f64 N -3) 1/3) 2)) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (.f64 (pow.f64 N -3) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (+.f64 (/.f64 -1/4 N) 1/3) 1) (pow.f64 N 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (+.f64 (/.f64 -1/4 N) 1/3)) (neg.f64 (pow.f64 N 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 -1/64 (pow.f64 N -3) 1/27) (pow.f64 N -3)) (+.f64 (/.f64 1/16 (.f64 N N)) (-.f64 1/9 (/.f64 -1/12 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (/.f64 1/16 (.f64 N N)) -1/9) (pow.f64 N -3)) (+.f64 (/.f64 -1/4 N) -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 N -3) (fma.f64 -1/64 (pow.f64 N -3) 1/27)) (+.f64 (/.f64 1/16 (.f64 N N)) (-.f64 1/9 (/.f64 -1/12 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 N -3) (+.f64 (/.f64 1/16 (.f64 N N)) -1/9)) (+.f64 (/.f64 -1/4 N) -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (+.f64 (/.f64 -1/4 N) 1/3) -1) (neg.f64 (pow.f64 N 3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 N -3) (+.f64 (/.f64 -1/4 N) 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (pow.f64 N -3) (+.f64 (/.f64 -1/4 N) 1/3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 (+.f64 (/.f64 -1/4 N) 1/3)) N) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 N -3/2) (sqrt.f64 (+.f64 (/.f64 -1/4 N) 1/3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (+.f64 (/.f64 -1/4 N) 1/3) 3) (pow.f64 (pow.f64 N 3) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (pow.f64 N -3) 3) (pow.f64 (+.f64 (/.f64 -1/4 N) 1/3) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (+.f64 (/.f64 -1/4 N) 1/3) 3) (pow.f64 (pow.f64 N -3) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 N 3) (+.f64 (/.f64 -1/4 N) 1/3)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 (pow.f64 N -6) (pow.f64 (+.f64 (/.f64 -1/4 N) 1/3) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (pow.f64 N -3)) (+.f64 (/.f64 -1/4 N) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 N -3) (+.f64 (/.f64 -1/4 N) 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 (pow.f64 N -3) 1/3)) (exp.f64 (/.f64 -1/4 (pow.f64 N 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (pow.f64 N -3) (+.f64 (/.f64 -1/4 N) 1/3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 (/.f64 -1/4 N) 1/3) 3) (pow.f64 (pow.f64 N 3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (pow.f64 N -3) 3) (pow.f64 (+.f64 (/.f64 -1/4 N) 1/3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (+.f64 (/.f64 -1/4 N) 1/3) 3) (pow.f64 (pow.f64 N -3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (pow.f64 N -3) (+.f64 (/.f64 -1/4 N) 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (pow.f64 N -3) (+.f64 (/.f64 -1/4 N) 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (fma.f64 -3 (log.f64 N) (log.f64 (+.f64 (/.f64 -1/4 N) 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (fma.f64 -3 (log.f64 N) (log.f64 (+.f64 (/.f64 -1/4 N) 1/3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 -1/4 (pow.f64 N 4)) (.f64 (pow.f64 N -3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 (pow.f64 N -3) 1/3) (/.f64 -1/4 (pow.f64 N 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N -3) (/.f64 -1/4 N) (.f64 (pow.f64 N -3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N -3) 1/3 (/.f64 -1/4 (pow.f64 N 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/4 (.f64 (/.f64 1 N) (pow.f64 N -3)) (.f64 (pow.f64 N -3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 -1/4 N) (pow.f64 N -3) (.f64 (pow.f64 N -3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/3 (pow.f64 N -3) (/.f64 -1/4 (pow.f64 N 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 1/16 (.f64 N N))) (.f64 (cbrt.f64 (/.f64 -1/4 N)) (pow.f64 N -3)) (.f64 (pow.f64 N -3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 N -6)) (.f64 (/.f64 1 N) (/.f64 -1/4 N)) (.f64 (pow.f64 N -3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 N -6)) (.f64 (/.f64 1 N) 1/3) (/.f64 -1/4 (pow.f64 N 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (/.f64 -1/4 N)) (.f64 (sqrt.f64 (/.f64 -1/4 N)) (pow.f64 N -3)) (.f64 (pow.f64 N -3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N -3/2) (.f64 (pow.f64 N -3/2) (/.f64 -1/4 N)) (.f64 (pow.f64 N -3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 N -3/2) (.f64 (pow.f64 N -3/2) 1/3) (/.f64 -1/4 (pow.f64 N 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 -1/4 (pow.f64 N 4)) 1 (.f64 (.f64 (pow.f64 N -3) 1/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (/.f64 -1/4 (pow.f64 N 4))) 2) (cbrt.f64 (/.f64 -1/4 (pow.f64 N 4))) (.f64 (pow.f64 N -3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 N -3) 1/3)) 2) (cbrt.f64 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(2) ((x fma.f64 (.f64 1/3 (pow.f64 N -3/2)) (pow.f64 N -3/2) (/.f64 -1/4 (pow.f64 N 4)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 N -3) (cbrt.f64 (/.f64 1/16 (.f64 N N)))) (cbrt.f64 (/.f64 -1/4 N)) (.f64 (pow.f64 N -3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (pow.f64 N -3) (sqrt.f64 (/.f64 -1/4 N))) (sqrt.f64 (/.f64 -1/4 N)) (.f64 (pow.f64 N -3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (/.f64 -1/4 N) (cbrt.f64 (pow.f64 N -6))) (/.f64 1 N) (.f64 (pow.f64 N -3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (/.f64 -1/4 N) (pow.f64 N -3/2)) (pow.f64 N -3/2) (.f64 (pow.f64 N -3) 1/3))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (/.f64 -1/4 N) 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (/.f64 1/16 (.f64 N N)) (+.f64 (/.f64 -1/4 N) -1/3)) (/.f64 1/9 (+.f64 (/.f64 -1/4 N) -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (/.f64 -1/4 N) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (/.f64 -1/4 N) 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 (/.f64 -1/4 N) 1/3)) (pow.f64 (cbrt.f64 (+.f64 (/.f64 -1/4 N) 1/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 -1/4 N) 1/3)) 2) (cbrt.f64 (+.f64 (/.f64 -1/4 N) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 (/.f64 -1/4 N) 1/3)) (sqrt.f64 (+.f64 (/.f64 -1/4 N) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 -1/64 (pow.f64 N -3) 1/27) (/.f64 1 (+.f64 (/.f64 1/16 (.f64 N N)) (-.f64 1/9 (/.f64 -1/12 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (/.f64 1/16 (.f64 N N)) -1/9) (/.f64 1 (+.f64 (/.f64 -1/4 N) -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (/.f64 1/16 (.f64 N N)) (-.f64 1/9 (/.f64 -1/12 N))) (fma.f64 -1/64 (pow.f64 N -3) 1/27)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (/.f64 -1/4 N) -1/3) (+.f64 (/.f64 1/16 (.f64 N N)) -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 -1/64 (pow.f64 N -3) 1/27) (+.f64 (/.f64 1/16 (.f64 N N)) (-.f64 1/9 (/.f64 -1/12 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 -1/64 (pow.f64 N -3) 1/27) (+.f64 1/9 (-.f64 (/.f64 1/16 (.f64 N N)) (/.f64 -1/12 N))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 1/16 (.f64 N N)) -1/9) (+.f64 (/.f64 -1/4 N) -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 -1/64 (pow.f64 N -3) 1/27)) (neg.f64 (+.f64 (/.f64 1/16 (.f64 N N)) (-.f64 1/9 (/.f64 -1/12 N)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (/.f64 1/16 (.f64 N N)) -1/9)) (neg.f64 (+.f64 (/.f64 -1/4 N) -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/9 (/.f64 1/16 (.f64 N N))) (-.f64 1/3 (/.f64 -1/4 N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (/.f64 -1/4 N) 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (/.f64 -1/4 N) 1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (/.f64 -1/4 N) 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (/.f64 -1/4 N) 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (/.f64 1/16 (.f64 N N)) (-.f64 1/9 (/.f64 -1/12 N))) (fma.f64 -1/64 (pow.f64 N -3) 1/27)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 (/.f64 -1/4 N) -1/3) (+.f64 (/.f64 1/16 (.f64 N N)) -1/9)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 -1/4 N) 1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 -1/4 N) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 -1/4 N) 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (/.f64 -1/4 N) 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (/.f64 -1/4 N) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (/.f64 -1/4 N) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (/.f64 -1/4 N) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (+.f64 (/.f64 -1/4 N) 1/3)) 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 (/.f64 1 N) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 -1/4 N) 1 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/4 (/.f64 1 (neg.f64 N)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 -1/4 N)) (cbrt.f64 (/.f64 1/16 (.f64 N N))) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 1/16 (*.f64 N N))) (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 (/.f64 1 N) -1/4 1/3)))))

simplify73.0ms (1.2%)

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

213 → 187

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))

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 12 to 9 computations (25% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite81.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

Outputs

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

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Counts

34 → 36

Calls

Call 1

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

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

eval193.0ms (3.3%)

Compiler: Compiled 7956 to 5569 computations (30% saved)

prune51.0ms (0.9%)

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	369	4	373
Fresh	1	0	1
Picked	0	1	1
Done	3	5	8
Total	373	10	383

Error

0.0b

Counts

383 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	31.9b	(-.f64 N (log.f64 N))
	56.5b	(-.f64 (+.f64 1 (/.f64 1 (+.f64 N 1/2))) 1)
	31.0b	(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (/.f64 (/.f64 (+.f64 (/.f64 -1/4 N) 1/3) (.f64 N N)) N)))
✓	32.7b	(neg.f64 (log.f64 N))
✓	26.8b	(/.f64 1 (+.f64 N 1/2))
	57.7b	2
✓	29.8b	(+.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))) (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))))
	46.0b	(/.f64 (+.f64 N (-.f64 (/.f64 1/3 N) 1/2)) (*.f64 N N))
✓	29.8b	(log.f64 (/.f64 (+.f64 N 1) N))
✓	30.3b	(/.f64 1 N)

Compiler

Compiled 88 to 64 computations (27.3% saved)

regimes46.0ms (0.8%)

Counts

21 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

20.0ms	N
11.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
9.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

Results

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

Compiler

Compiled 218 to 140 computations (35.8% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.011671197405974e-5	0.0057746571257952795

Compiler

Compiled 12 to 9 computations (25% saved)

regimes42.0ms (0.7%)

Counts

20 → 2

Calls

Call 1

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

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

Calls

3 calls:

19.0ms	N
9.0ms	(-.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	2	`N`
0.0b	2	`(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))`
0.0b	2	`(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))`

Compiler

Compiled 203 to 129 computations (36.5% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.011671197405974e-5	0.0057746571257952795

Compiler

Compiled 12 to 9 computations (25% saved)

regimes22.0ms (0.4%)

Counts

15 → 2

Calls

Call 1

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

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

Calls

1 calls:

18.0ms

Results

Error	Segments	Branch
0.3b	2	`N`

Compiler

Compiled 129 to 83 computations (35.7% saved)

bsearch30.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
30.0ms	0.5243713124160303	172.67093588470735

Compiler

Compiled 12 to 9 computations (25% saved)

regimes20.0ms (0.3%)

Counts

14 → 2

Calls

Call 1

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

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

Calls

1 calls:

16.0ms

Results

Error	Segments	Branch
0.5b	2	`N`

Compiler

Compiled 125 to 82 computations (34.4% saved)

bsearch24.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
23.0ms	0.5243713124160303	172.67093588470735

Compiler

Compiled 12 to 9 computations (25% saved)

regimes25.0ms (0.4%)

Counts

13 → 1

Calls

Call 1

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

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

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
26.8b	1	`N`

Compiler

Compiled 122 to 80 computations (34.4% saved)

regimes8.0ms (0.1%)

Counts

3 → 2

Calls

Call 1

Inputs
2
N
(/.f64 1 N)

Outputs
2
(/.f64 1 N)

Calls

1 calls:

7.0ms

Results

Error	Segments	Branch
27.5b	2	`N`

Compiler

Compiled 8 to 5 computations (37.5% saved)

bsearch26.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
25.0ms	7.357464671497419e-7	0.5243713124160303

Compiler

Compiled 12 to 9 computations (25% saved)

regimes4.0ms (0.1%)

Accuracy

Total -3.3b remaining (-5.8%)

Threshold costs -3.3b (-5.8%)

Counts

2 → 1

Calls

Call 1

Inputs
2
N

Outputs
2

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
57.7b	1	`N`

Compiler

Compiled 5 to 3 computations (40% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	231
1	54	231
2	58	231
3	59	231

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 7378697629483821/147573952589676412928) (+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (/.f64 (/.f64 (+.f64 (/.f64 -1/4 N) 1/3) (.f64 N N)) N))) (+.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))) (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))))
(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 7378697629483821/147573952589676412928) (+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (/.f64 (/.f64 (+.f64 (/.f64 -1/4 N) 1/3) (.f64 N N)) N))) (log.f64 (/.f64 (+.f64 N 1) N)))
(if (<=.f64 N 590389611800153/1125899906842624) (-.f64 N (log.f64 N)) (+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (/.f64 (/.f64 (+.f64 (/.f64 -1/4 N) 1/3) (.f64 N N)) N))))
(if (<=.f64 N 590389611800153/1125899906842624) (neg.f64 (log.f64 N)) (+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (/.f64 (/.f64 (+.f64 (/.f64 -1/4 N) 1/3) (.f64 N N)) N))))
(/.f64 1 (+.f64 N 1/2))
(if (<=.f64 N 6948928912715387/9444732965739290427392) 2 (/.f64 1 N))
2

Outputs
(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 7378697629483821/147573952589676412928) (+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (/.f64 (/.f64 (+.f64 (/.f64 -1/4 N) 1/3) (.f64 N N)) N))) (+.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N))) (log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))))
(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 7378697629483821/147573952589676412928) (+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (/.f64 (/.f64 (+.f64 (/.f64 -1/4 N) 1/3) (.f64 N N)) N))) (log.f64 (/.f64 (+.f64 N 1) N)))
(if (<=.f64 N 590389611800153/1125899906842624) (-.f64 N (log.f64 N)) (+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (/.f64 (/.f64 (+.f64 (/.f64 -1/4 N) 1/3) (.f64 N N)) N))))
(if (<=.f64 N 590389611800153/1125899906842624) (neg.f64 (log.f64 N)) (+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (.f64 N N)) (/.f64 (/.f64 (+.f64 (/.f64 -1/4 N) 1/3) (.f64 N N)) N))))
(/.f64 1 (+.f64 N 1/2))
(if (<=.f64 N 6948928912715387/9444732965739290427392) 2 (/.f64 1 N))
2

Compiler

Compiled 161 to 111 computations (31.1% saved)

soundness202.0ms (3.4%)

Algorithm

3×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	saturated
1×	node limit
1×	saturated

Compiler

Compiled 863 to 724 computations (16.1% saved)

end130.0ms (2.2%)

Compiler: Compiled 155 to 99 computations (36.1% saved)