Details

analyze3.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.8s (36.7%)

Results

1.2s	2040×	body	1024	valid
913.0ms	4897×	body	256	valid
305.0ms	1051×	body	512	valid
303.0ms	268×	body	2048	valid

Bogosity

preprocess20.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

30.9b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.9b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 6 to 4 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.5b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 11 to 4 computations (63.6% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite60.0ms (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)))))))

simplify114.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

47 → 50

Calls

Call 1

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

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

eval11.0ms (0.1%)

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

prune16.0ms (0.2%)

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
▶	31.0b	(-.f64 (/.f64 1 N) (/.f64 (/.f64 1/2 N) N))
	30.8b	(log.f64 (/.f64 (+.f64 N 1) N))
▶	31.8b	(-.f64 N (log.f64 N))
	31.1b	(pow.f64 (sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 2)
▶	30.7b	(+.f64 (/.f64 1 N) (.f64 (/.f64 1 (.f64 N N)) (-.f64 (/.f64 1/3 N) 1/2)))
▶	32.4b	(neg.f64 (log.f64 N))
▶	29.7b	(/.f64 1 N)

Compiler

Compiled 110 to 80 computations (27.3% saved)

localize3.0ms (0%)

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

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 24 to 16 computations (33.3% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite115.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 294

Calls

Call 1

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

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

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

simplify49.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

318 → 300

Calls

Call 1

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

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

localize29.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 50 to 32 computations (36% saved)

series10.0ms (0.1%)

Counts

3 → 24

Calls

9 calls:

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

rewrite119.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

434×	`log-prod_binary64`
373×	`prod-exp_binary64`
338×	`exp-prod_binary64`
281×	`pow-prod-down_binary64`
256×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	222	21
2	2800	21

Stop Event

1×	node limit

Counts

3 → 161

Calls

Call 1

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

Outputs

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

simplify92.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

704×	`distribute-neg-frac_binary64`
590×	`fma-neg_binary64`
536×	`unswap-sqr_binary64`
534×	`fma-def_binary64`
478×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	249
1	41	249
2	82	249
3	181	249
4	545	249
5	2438	249
6	5502	249
7	7974	249

Stop Event

1×	node limit

Counts

185 → 168

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))))

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

localize112.0ms (1.5%)

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

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 8 to 3 computations (62.5% saved)

series15.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
9.0ms	N	@	0	(-.f64 N (log.f64 N))
3.0ms	N	@	-inf	(-.f64 N (log.f64 N))
2.0ms	N	@	inf	(-.f64 N (log.f64 N))

rewrite294.0ms (3.9%)

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)))))))

simplify238.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

47 → 42

Calls

Call 1

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

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

eval299.0ms (4%)

Compiler: Compiled 11921 to 8647 computations (27.5% saved)

prune148.0ms (2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	507	3	510
Fresh	0	2	2
Picked	0	1	1
Done	2	2	4
Total	509	8	517

Error

0.0b

Counts

517 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.7b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
	61.2b	N
▶	31.0b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
✓	32.4b	(neg.f64 (log.f64 N))
✓	31.8b	(-.f64 N (log.f64 N))
▶	31.1b	(pow.f64 (sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 2)
▶	30.8b	(log.f64 (/.f64 (+.f64 N 1) N))
✓	29.7b	(/.f64 1 N)

Compiler

Compiled 53 to 38 computations (28.3% saved)

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.4b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 17 to 11 computations (35.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite50.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	127	8
2	1707	8

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(log.f64 (/.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))))))))

simplify39.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

37 → 40

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))))

localize22.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 45 to 32 computations (28.9% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite79.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

652×	`unpow-prod-down_binary64`
447×	`log-prod_binary64`
251×	`pow-prod-down_binary64`
240×	`pow2_binary64`
199×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
1	188	23
2	2626	23

Stop Event

1×	node limit

Counts

2 → 153

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (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 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) (/.f64 1 N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2))) (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) N) 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) N) 4)) (cbrt.f64 (*.f64 (+.f64 (/.f64 1/3 N) -1/2) (pow.f64 N -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)) 2) (*.f64 (cbrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)) (/.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) N) (/.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)) (*.f64 (sqrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)) (/.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 1/2 (neg.f64 (/.f64 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-1/2)) N) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) 1) 1) (/.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) N))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) 2) (pow.f64 (cbrt.f64 N) 2)) 1) (cbrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (pow.f64 (cbrt.f64 N) 2)) 1) (pow.f64 (/.f64 (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (cbrt.f64 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) 2) (sqrt.f64 N)) 1) (pow.f64 (/.f64 (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) (sqrt.f64 N)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (pow.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) 2) (+.f64 (/.f64 1/3 N) -1/2)) 1/3) (cbrt.f64 (/.f64 1 N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) (cbrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N))) 2) 1/3) (cbrt.f64 (cbrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N))) 2) 3) (cbrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 N (+.f64 (/.f64 1/3 N) -1/2))) 2) -1) (cbrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) -2) -1) (pow.f64 (/.f64 N (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 N) 2) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) 2)) -1) (pow.f64 (/.f64 (cbrt.f64 N) (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (sqrt.f64 N) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2)) 2)) -1) (pow.f64 (/.f64 (sqrt.f64 N) (cbrt.f64 (+.f64 (/.f64 1/3 N) -1/2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (+.f64 (/.f64 1/3 N) -1/2) -1/2) -1) (pow.f64 (/.f64 N (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (pow.f64 (cbrt.f64 N) 2) (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2))) -1) (pow.f64 (/.f64 (cbrt.f64 N) (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 (sqrt.f64 N) (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2))) -1) (pow.f64 (/.f64 (sqrt.f64 N) (sqrt.f64 (+.f64 (/.f64 1/3 N) -1/2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 N (fma.f64 1/27 (pow.f64 N -3) -1/8)) -1) (/.f64 1 (-.f64 (fma.f64 1/9 (pow.f64 N -2) 1/4) (/.f64 -1/6 N))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 N (fma.f64 1/9 (pow.f64 N -2) -1/4)) -1) (/.f64 1 (+.f64 (/.f64 1/3 N) 1/2)))))) (#(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) 2) 1/2)))) (#(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))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 N (+.f64 (/.f64 1/3 N) -1/2))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N)) 1) 1))))))

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

790×	`distribute-neg-frac_binary64`
536×	`unswap-sqr_binary64`
393×	`fma-neg_binary64`
377×	`distribute-rgt-neg-in_binary64`
356×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	297
1	55	297
2	104	297
3	231	297
4	711	297
5	3276	297
6	6109	297

Stop Event

1×	node limit

Counts

177 → 163

Calls

Call 1

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

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

localize17.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 14 computations (26.3% saved)

series4.0ms (0%)

Counts

1 → 12

Calls

3 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)

rewrite96.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

43 → 36

Calls

Call 1

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

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

localize20.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N)))
✓	0.3b	(pow.f64 (sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 2)
	2.5b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 26 to 8 computations (69.2% saved)

series17.0ms (0.2%)

Counts

2 → 8

Calls

6 calls:

Time	Variable		Point	Expression
9.0ms	N	@	-inf	(pow.f64 (sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 2)
3.0ms	N	@	inf	(pow.f64 (sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 2)
2.0ms	N	@	0	(pow.f64 (sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 2)
1.0ms	N	@	0	(sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N)))
1.0ms	N	@	-inf	(sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N)))

rewrite80.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

727×	`pow1_binary64`
679×	`add-log-exp_binary64`
678×	`expm1-log1p-u_binary64`
677×	`log1p-expm1-u_binary64`
663×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	171	18
2	1886	18

Stop Event

1×	node limit

Counts

2 → 61

Calls

Call 1

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

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

simplify53.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

791×	`associate-/l*_binary64`
480×	`associate-/r*_binary64`
324×	`associate-/r/_binary64`
316×	`fma-def_binary64`
290×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	421
1	175	348
2	603	320
3	2918	250

Stop Event

1×	node limit

Counts

69 → 77

Calls

Call 1

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

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

eval312.0ms (4.1%)

Compiler: Compiled 7091 to 4733 computations (33.3% saved)

prune226.0ms (3%)

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	400	2	402
Fresh	0	1	1
Picked	0	1	1
Done	0	6	6
Total	400	10	410

Error

Counts

410 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.7b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
	61.2b	N
✓	31.0b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
▶	61.8b	(-.f64 (+.f64 1 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)) 1)
✓	32.4b	(neg.f64 (log.f64 N))
▶	31.0b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N))))
✓	31.8b	(-.f64 N (log.f64 N))
✓	31.1b	(pow.f64 (sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 2)
✓	30.8b	(log.f64 (/.f64 (+.f64 N 1) N))
✓	29.7b	(/.f64 1 N)

Compiler

Compiled 83 to 62 computations (25.3% saved)

localize52.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(cbrt.f64 (/.f64 (+.f64 N 1) N))
✓	0.2b	(pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)
✓	2.4b	(log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)))
✓	2.4b	(log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2))

Compiler

Compiled 59 to 43 computations (27.1% saved)

series13.0ms (0.2%)

Counts

4 → 32

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	N	@	-inf	(log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2))
2.0ms	N	@	0	(log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2))
2.0ms	N	@	-inf	(log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)))
1.0ms	N	@	0	(log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)))
1.0ms	N	@	inf	(log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2))

rewrite70.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	46
1	207	46
2	2496	46

Stop Event

1×	node limit

Counts

4 → 97

Calls

Call 1

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

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

simplify176.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-def_binary64`
413×	`associate-l_binary64`
373×	`associate-r_binary64`
363×	`distribute-rgt-in_binary64`
326×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	175	1083
1	533	953
2	1659	870
3	6223	850

Stop Event

1×	node limit

Counts

129 → 155

Calls

Call 1

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

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

localize18.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
✓	2.4b	(-.f64 (+.f64 1 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)) 1)

Compiler

Compiled 39 to 30 computations (23.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite67.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

600×	`prod-diff_binary64`
523×	`fma-def_binary64`
422×	`log-prod_binary64`
248×	`pow2_binary64`
230×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	215	10
2	3184	10

Stop Event

1×	node limit

Counts

1 → 108

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N) 0)))) (#(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 0 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 1 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)))) (log.f64 (sqrt.f64 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simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

120 → 113

Calls

Call 1

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

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

eval943.0ms (12.5%)

Compiler: Compiled 7761 to 6151 computations (20.7% saved)

prune83.0ms (1.1%)

Pruning

10 alts after pruning (1 fresh and 9 done)

	Pruned	Kept	Total
New	349	0	349
Fresh	0	1	1
Picked	0	1	1
Done	0	8	8
Total	349	10	359

Error

Counts

359 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.7b	(+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N))
	61.2b	N
✓	31.0b	(/.f64 (+.f64 1 (/.f64 -1/2 N)) N)
✓	61.8b	(-.f64 (+.f64 1 (/.f64 (+.f64 1 (/.f64 -1/2 N)) N)) 1)
✓	32.4b	(neg.f64 (log.f64 N))
✓	31.0b	(+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N)) 2)) (log.f64 (cbrt.f64 (/.f64 (+.f64 N 1) N))))
✓	31.8b	(-.f64 N (log.f64 N))
✓	31.1b	(pow.f64 (sqrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 2)
✓	30.8b	(log.f64 (/.f64 (+.f64 N 1) N))
✓	29.7b	(/.f64 1 N)

Compiler

Compiled 83 to 62 computations (25.3% saved)

regimes26.0ms (0.3%)

Counts

14 → 2

Calls

Call 1

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

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

Calls

2 calls:

15.0ms	N
6.0ms	(-.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))`

Compiler

Compiled 120 to 79 computations (34.2% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	4.3133141502949e-10	0.2553555237958183

Compiler

Compiled 12 to 9 computations (25% saved)

regimes15.0ms (0.2%)

Counts

9 → 2

Calls

Call 1

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

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

Calls

1 calls:

11.0ms

Results

Error	Segments	Branch
0.2b	2	`N`

Compiler

Compiled 69 to 47 computations (31.9% saved)

bsearch28.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
28.0ms	2.2078869502073876e-9	3.437365282383633

Compiler

Compiled 12 to 9 computations (25% saved)

regimes15.0ms (0.2%)

Counts

8 → 2

Calls

Call 1

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

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

Calls

1 calls:

10.0ms

Results

Error	Segments	Branch
0.3b	2	`N`

Compiler

Compiled 65 to 46 computations (29.2% saved)

bsearch27.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
27.0ms	2.2078869502073876e-9	3.437365282383633

Compiler

Compiled 12 to 9 computations (25% saved)

regimes8.0ms (0.1%)

Accuracy

Total -33.1b remaining (-111.6%)

Threshold costs -33.1b (-111.6%)

Counts

7 → 1

Calls

Call 1

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

Outputs
(/.f64 1 N)

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
29.7b	1	`N`

Compiler

Compiled 62 to 44 computations (29% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	101
1	41	101
2	45	101
3	46	101

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 4835703278458517/9671406556917033397649408) (/.f64 (+.f64 1 (/.f64 -1/2 N)) N) (log.f64 (/.f64 (+.f64 N 1) N)))
(if (<=.f64 N 1334585770447955/604462909807314587353088) (-.f64 N (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)))
(if (<=.f64 N 1334585770447955/604462909807314587353088) (neg.f64 (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)))
(/.f64 1 N)
N

Outputs
(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 4835703278458517/9671406556917033397649408) (/.f64 (+.f64 1 (/.f64 -1/2 N)) N) (log.f64 (/.f64 (+.f64 N 1) N)))
(if (<=.f64 N 1334585770447955/604462909807314587353088) (-.f64 N (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)))
(if (<=.f64 N 1334585770447955/604462909807314587353088) (-.f64 N (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 -1/2 (/.f64 1/3 N)) N) N)))
(if (<=.f64 N 1334585770447955/604462909807314587353088) (neg.f64 (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 (/.f64 1/3 N) -1/2) N) N)))
(if (<=.f64 N 1334585770447955/604462909807314587353088) (neg.f64 (log.f64 N)) (+.f64 (/.f64 1 N) (/.f64 (/.f64 (+.f64 -1/2 (/.f64 1/3 N)) N) N)))
(/.f64 1 N)
N

Compiler

Compiled 73 to 52 computations (28.8% saved)

soundness109.0ms (1.5%)

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 100 to 75 computations (25% saved)

end98.0ms (1.3%)

Compiler: Compiled 69 to 46 computations (33.3% saved)

Details

analyze3.0ms (0%)

sample2.8s (36.7%)

preprocess20.0ms (0.3%)

simplify15.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize7.0ms (0.1%)

series2.0ms (0%)

rewrite60.0ms (0.8%)

simplify114.0ms (1.5%)

eval11.0ms (0.1%)

prune16.0ms (0.2%)

localize3.0ms (0%)

localize11.0ms (0.1%)

series3.0ms (0%)

rewrite115.0ms (1.5%)

simplify49.0ms (0.7%)

localize29.0ms (0.4%)

series10.0ms (0.1%)

rewrite119.0ms (1.6%)

simplify92.0ms (1.2%)

localize112.0ms (1.5%)

localize9.0ms (0.1%)

series15.0ms (0.2%)

rewrite294.0ms (3.9%)

simplify238.0ms (3.2%)

eval299.0ms (4%)

prune148.0ms (2%)

localize10.0ms (0.1%)

series2.0ms (0%)

rewrite50.0ms (0.7%)

simplify39.0ms (0.5%)

localize22.0ms (0.3%)

series3.0ms (0%)

rewrite79.0ms (1%)

simplify65.0ms (0.9%)

localize17.0ms (0.2%)

series4.0ms (0%)

rewrite96.0ms (1.3%)

simplify58.0ms (0.8%)

localize20.0ms (0.3%)

series17.0ms (0.2%)

rewrite80.0ms (1.1%)

simplify53.0ms (0.7%)

eval312.0ms (4.1%)

prune226.0ms (3%)

localize52.0ms (0.7%)

series13.0ms (0.2%)

rewrite70.0ms (0.9%)

simplify176.0ms (2.3%)

localize18.0ms (0.2%)

series1.0ms (0%)

rewrite67.0ms (0.9%)

simplify66.0ms (0.9%)

eval943.0ms (12.5%)

prune83.0ms (1.1%)

regimes26.0ms (0.3%)

bsearch0.0ms (0%)

regimes15.0ms (0.2%)

bsearch28.0ms (0.4%)

regimes15.0ms (0.2%)

bsearch27.0ms (0.4%)

regimes8.0ms (0.1%)

simplify6.0ms (0.1%)

soundness109.0ms (1.5%)

end98.0ms (1.3%)

Profiling