Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	50%	25%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.0s (75.3%)

Results

896.0ms	2112×	body	1024	valid
516.0ms	4298×	body	128	valid
326.0ms	1074×	body	512	valid
148.0ms	245×	body	2048	valid
106.0ms	527×	body	256	valid

preprocess18.0ms (0.7%)

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	164	8
9	200	8
10	226	8
11	228	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 8 to 6 computations (25% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	33	8
5	50	8
6	87	8
7	123	8
8	164	8
9	200	8
10	226	8
11	228	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))

prune3.0ms (0.1%)

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

31.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.4b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 25 to 16 computations (36% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.6b	(-.f64 (log1p.f64 N) (log.f64 N))

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite37.0ms (1.4%)

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	1449	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 (-.f64 (/.f64 (+.f64 N 1) N) 1))))) (#(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 exp.f64 (log.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 (-.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 (-.f64 (/.f64 (+.f64 N 1) N) 1))))) (#(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 exp.f64 (log.f64 (-.f64 (log1p.f64 N) (log.f64 N))))))))

simplify23.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
458×	`fma-neg_binary64`
425×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`
169×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	192
1	95	188
2	237	185
3	643	181
4	2042	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 N (.f64 N -1/2)) (log.f64 N)))
(-.f64 (fma.f64 N (*.f64 N -1/2) N) (log.f64 N))
(fma.f64 N (*.f64 N -1/2) (-.f64 N (log.f64 N)))
(+.f64 N (+.f64 (.f64 -1 (log.f64 N)) (+.f64 (.f64 1/3 (pow.f64 N 3)) (*.f64 -1/2 (pow.f64 N 2)))))
(+.f64 N (fma.f64 -1 (log.f64 N) (fma.f64 1/3 (pow.f64 N 3) (.f64 -1/2 (.f64 N N)))))
(+.f64 N (-.f64 (fma.f64 -1/2 (.f64 N N) (.f64 1/3 (pow.f64 N 3))) (log.f64 N)))
(+.f64 (-.f64 N (log.f64 N)) (.f64 (.f64 N N) (+.f64 -1/2 (*.f64 N 1/3))))
(fma.f64 N (*.f64 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 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N))))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/2 (*.f64 N N))))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N))))
(-.f64 (/.f64 1 N) (-.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/3 (pow.f64 N 3))))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.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 (.f64 1/4 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4)))))
(+.f64 (/.f64 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 1 N) (/.f64 -1/4 (pow.f64 N 4))) (-.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/3 (pow.f64 N 3))))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.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 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 1/2 (*.f64 N N))))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/2 (*.f64 N N))))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N))))
(-.f64 (/.f64 1 N) (-.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/3 (pow.f64 N 3))))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.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 (.f64 1/4 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
(+.f64 (/.f64 1 N) (-.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4)))))
(+.f64 (/.f64 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 1 N) (/.f64 -1/4 (pow.f64 N 4))) (-.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/3 (pow.f64 N 3))))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N))))

prune33.0ms (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	4	51

Error

0.0b

Counts

51 → 4

Alt Table

Status	Error	Program
	32.0b	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
	31.2b	(log.f64 (/.f64 (+.f64 N 1) N))
	60.9b	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
▶	29.7b	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N))))

Compiler

Compiled 743 to 358 computations (51.8% saved)

localize15.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 1/2 N) N)
✓	0.2b	(/.f64 -1/4 (pow.f64 N 4))
✓	0.5b	(/.f64 1/3 (pow.f64 N 3))
✓	19.0b	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N))))

series6.0ms (0.2%)

Counts

4 → 24

Calls

12 calls:

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

rewrite39.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

212×	`add-sqr-sqrt_binary64`
204×	`add-log-exp_binary64`
204×	`log1p-expm1-u_binary64`
204×	`expm1-log1p-u_binary64`
203×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	52
1	438	50

Stop Event

1×	node limit

Counts

4 → 81

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))) 2) (cbrt.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))) (sqrt.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 1/27 (pow.f64 (pow.f64 N -3) 3)) (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 3)) (+.f64 (/.f64 1/9 (pow.f64 N 6)) (-.f64 (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 2) (.f64 (.f64 1/3 (pow.f64 N -3)) (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (/.f64 1/9 (pow.f64 N 6)) (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 2)) (-.f64 (.f64 1/3 (pow.f64 N -3)) (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (.f64 1/27 (pow.f64 (pow.f64 N -3) 3)) (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 3))) (neg.f64 (+.f64 (/.f64 1/9 (pow.f64 N 6)) (-.f64 (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 2) (.f64 (.f64 1/3 (pow.f64 N -3)) (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (/.f64 1/9 (pow.f64 N 6)) (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 2))) (neg.f64 (-.f64 (.f64 1/3 (pow.f64 N -3)) (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/3 (pow.f64 N -3) (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 1/3 (pow.f64 N -3)) (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) (.f64 1/3 (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 1/9 (pow.f64 N 6))) (/.f64 (cbrt.f64 1/3) N) (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 2)) (cbrt.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))) (.f64 1/3 (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 1/3) (pow.f64 N 3/2)) (/.f64 (sqrt.f64 1/3) (pow.f64 N 3/2)) (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 (pow.f64 N -1/2) (sqrt.f64 (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))) (hypot.f64 (pow.f64 N -1/2) (sqrt.f64 (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))) (.f64 1/3 (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (+.f64 (fma.f64 1/3 (pow.f64 N -3) (pow.f64 N -1)) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 1/3 (pow.f64 N -3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/3 (pow.f64 N -3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 1/3 (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/9 (pow.f64 N 6))) (/.f64 (cbrt.f64 1/3) N))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 1/3) (pow.f64 N 3/2)) (/.f64 (sqrt.f64 1/3) (pow.f64 N 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/3 (pow.f64 N -3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (cbrt.f64 1/3) N) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 1/3) (pow.f64 N 3/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/27 (pow.f64 (pow.f64 N -3) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 N 3) 1/3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/9 (pow.f64 N 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 1/3) (pow.f64 N -3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 1/3 (pow.f64 N -3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 1/27 (pow.f64 (pow.f64 N -3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 1/3 (pow.f64 N -3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 1/3 (pow.f64 N -3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 1/3 (pow.f64 N -3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 1/3 (pow.f64 N -3))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 -1/4 (pow.f64 N -4)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 -1/4 (pow.f64 N -4)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/4 (pow.f64 N -4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/16 (pow.f64 N 8))) (cbrt.f64 (.f64 -1/4 (pow.f64 N -4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 -1/4) (.f64 N N)) (/.f64 (sqrt.f64 -1/4) (.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 -1/4 (pow.f64 N -4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 -1/4 (pow.f64 N -4))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 -1/4) (.f64 N N)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 -1/64 (pow.f64 (pow.f64 N -4) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 N 4) -1/4) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/16 (pow.f64 N 8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/4) (pow.f64 N -4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 -1/4 (pow.f64 N -4)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 -1/64 (pow.f64 (pow.f64 N -4) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 -1/4 (pow.f64 N -4))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 -1/4 (pow.f64 N -4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 -1/4 (pow.f64 N -4))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 -1/4 (pow.f64 N -4))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1/2 (.f64 N N)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1/2 (.f64 N N)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1/2 N) (pow.f64 N -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1/4 (pow.f64 N 4))) (cbrt.f64 (/.f64 1/2 (.f64 N 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 pow.f64 (/.f64 1/2 (.f64 N N)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/2 (.f64 N N))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 1/2) N) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/8 (pow.f64 N 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 N (/.f64 1/2 N)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/4 (pow.f64 N 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/2 (.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1/2 (.f64 N N)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 1/8 (pow.f64 N 6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/2 (.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/2 (.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/2 (.f64 N N))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 1/2 (.f64 N N))) 1))))))

simplify22.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

453×	`times-frac_binary64`
337×	`fma-def_binary64`
331×	`associate-l_binary64`
315×	`associate-/l/_binary64`
287×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	303
1	79	303
2	178	303
3	425	303
4	1337	303

Stop Event

1×	node limit

Counts

105 → 95

Calls

Call 1

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

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

prune99.0ms (3.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	93	6	99

Error

0.0b

Counts

99 → 6

Alt Table

Status	Error	Program
	60.9b	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
	51.6b	(/.f64 (+.f64 (.f64 1/27 (pow.f64 (pow.f64 N -3) 3)) (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 3)) (+.f64 (/.f64 1/9 (pow.f64 N 6)) (-.f64 (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 2) (.f64 (.f64 1/3 (pow.f64 N -3)) (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (*.f64 N N))))))))
	32.0b	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
▶	31.2b	(log.f64 (/.f64 (+.f64 N 1) N))
✓	29.7b	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N))))
	45.6b	(fma.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 2)) (cbrt.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))) (*.f64 1/3 (pow.f64 N -3)))

Compiler

Compiled 2665 to 2019 computations (24.2% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 N 1) N)
✓	2.5b	(log.f64 (/.f64 (+.f64 N 1) N))

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite38.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

680×	`pow1_binary64`
635×	`log1p-expm1-u_binary64`
635×	`expm1-log1p-u_binary64`
634×	`add-log-exp_binary64`
64×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	127	15
2	1703	15

Stop Event

1×	node limit

Counts

2 → 60

Calls

Call 1

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

Outputs

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

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

simplify23.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-def_binary64`
458×	`fma-neg_binary64`
425×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`
169×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	37	261
1	97	257
2	239	254
3	647	250
4	2042	250

Stop Event

1×	node limit

Counts

84 → 77

Calls

Call 1

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

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

prune38.0ms (1.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	77	6	83

Error

0.0b

Counts

83 → 6

Alt Table

Status	Error	Program
	60.9b	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
	51.6b	(/.f64 (+.f64 (.f64 1/27 (pow.f64 (pow.f64 N -3) 3)) (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 3)) (+.f64 (/.f64 1/9 (pow.f64 N 6)) (-.f64 (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 2) (.f64 (.f64 1/3 (pow.f64 N -3)) (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (*.f64 N N))))))))
▶	32.0b	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
✓	31.2b	(log.f64 (/.f64 (+.f64 N 1) N))
✓	29.7b	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N))))
	45.6b	(fma.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 2)) (cbrt.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))) (*.f64 1/3 (pow.f64 N -3)))

Compiler

Compiled 1144 to 724 computations (36.7% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (log1p.f64 N))
✓	31.7b	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))

series9.0ms (0.3%)

Counts

2 → 17

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	N	@	-inf	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
1.0ms	N	@	0	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
1.0ms	N	@	inf	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
1.0ms	N	@	-inf	(sqrt.f64 (log1p.f64 N))
1.0ms	N	@	inf	(sqrt.f64 (log1p.f64 N))

rewrite32.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

527×	`pow1_binary64`
486×	`add-log-exp_binary64`
485×	`expm1-log1p-u_binary64`
484×	`log1p-expm1-u_binary64`
474×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	139	13
2	1630	13

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

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

Outputs

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

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

simplify33.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-def_binary64`
353×	`associate-+l+_binary64`
336×	`associate-/r*_binary64`
280×	`associate-l_binary64`
254×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	122	1420
1	387	1160
2	1333	910

Stop Event

1×	node limit

Counts

59 → 75

Calls

Call 1

Inputs
(*.f64 -1 (log.f64 N))
(-.f64 (pow.f64 (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N)))) 2) (.f64 -1 (log.f64 (/.f64 1 N))))
(-.f64 (+.f64 (pow.f64 (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N)))) 2) (/.f64 1 N)) (.f64 -1 (log.f64 (/.f64 1 N))))
(-.f64 (+.f64 (.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) 2)) (pow.f64 N 2))) (+.f64 (pow.f64 (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N)))) 2) (+.f64 (/.f64 1 N) (.f64 1/4 (/.f64 1 (.f64 (pow.f64 N 2) (pow.f64 (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N)))) 2))))))) (*.f64 -1 (log.f64 (/.f64 1 N))))
(-.f64 (+.f64 (.f64 1/4 (/.f64 1 (.f64 (pow.f64 N 2) (pow.f64 (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N)))) 2)))) (+.f64 (.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) 2)) (pow.f64 N 2))) (+.f64 (pow.f64 (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N)))) 2) (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3))))))) (.f64 -1 (log.f64 (/.f64 1 N))))
(/.f64 1 N)
(+.f64 (/.f64 1/4 (.f64 (pow.f64 N 2) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (+.f64 (/.f64 1 N) (.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (pow.f64 N 2)))))
(+.f64 (.f64 -1 (/.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) (.f64 -1 (+.f64 (.f64 1/2 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))) 1/3))) (pow.f64 N 3))) (+.f64 (/.f64 1 N) (+.f64 (.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (.f64 -1/2 (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))) 2)) (pow.f64 N 2))) (.f64 1/4 (/.f64 1 (.f64 (pow.f64 N 2) (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))))))
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(sqrt.f64 (*.f64 -1 (log.f64 (/.f64 1 N))))
(+.f64 (.f64 1/2 (/.f64 1 (.f64 N (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N))))))) (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N)))))
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(sqrt.f64 (+.f64 (log.f64 -1) (*.f64 -1 (log.f64 (/.f64 -1 N)))))
(+.f64 (.f64 1/2 (.f64 (/.f64 1 N) (sqrt.f64 (/.f64 1 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N)))))))) (sqrt.f64 (+.f64 (log.f64 -1) (.f64 -1 (log.f64 (/.f64 -1 N))))))
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Outputs
(*.f64 -1 (log.f64 N))
(neg.f64 (log.f64 N))
(-.f64 (pow.f64 (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N)))) 2) (.f64 -1 (log.f64 (/.f64 1 N))))
(-.f64 (pow.f64 (sqrt.f64 (neg.f64 (neg.f64 (log.f64 N)))) 2) (neg.f64 (neg.f64 (log.f64 N))))
(-.f64 (log.f64 N) (log.f64 N))
0
(-.f64 (+.f64 (pow.f64 (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N)))) 2) (/.f64 1 N)) (.f64 -1 (log.f64 (/.f64 1 N))))
(+.f64 (pow.f64 (sqrt.f64 (neg.f64 (neg.f64 (log.f64 N)))) 2) (-.f64 (/.f64 1 N) (neg.f64 (neg.f64 (log.f64 N)))))
(+.f64 (/.f64 1 N) (-.f64 (log.f64 N) (log.f64 N)))
(+.f64 (/.f64 1 N) 0)
(-.f64 (+.f64 (.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N))))) 2)) (pow.f64 N 2))) (+.f64 (pow.f64 (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N)))) 2) (+.f64 (/.f64 1 N) (.f64 1/4 (/.f64 1 (.f64 (pow.f64 N 2) (pow.f64 (sqrt.f64 (.f64 -1 (log.f64 (/.f64 1 N)))) 2))))))) (*.f64 -1 (log.f64 (/.f64 1 N))))
(-.f64 (fma.f64 -1 (/.f64 (+.f64 1/2 (pow.f64 (/.f64 1/2 (sqrt.f64 (neg.f64 (neg.f64 (log.f64 N))))) 2)) (.f64 N N)) (+.f64 (+.f64 (/.f64 1 N) (pow.f64 (sqrt.f64 (neg.f64 (neg.f64 (log.f64 N)))) 2)) (/.f64 1/4 (.f64 (pow.f64 (sqrt.f64 (neg.f64 (neg.f64 (log.f64 N)))) 2) (*.f64 N N))))) (neg.f64 (neg.f64 (log.f64 N))))
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(+.f64 (-.f64 (/.f64 (/.f64 1/4 (.f64 N N)) (log.f64 N)) (/.f64 (+.f64 1/2 (/.f64 1/4 (log.f64 N))) (.f64 N N))) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) 0)))
(/.f64 1 N)
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prune77.0ms (2.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	111	6	117

Error

0.0b

Counts

117 → 6

Alt Table

Status	Error	Program
	60.9b	(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
	51.6b	(/.f64 (+.f64 (.f64 1/27 (pow.f64 (pow.f64 N -3) 3)) (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 3)) (+.f64 (/.f64 1/9 (pow.f64 N 6)) (-.f64 (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 2) (.f64 (.f64 1/3 (pow.f64 N -3)) (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (*.f64 N N))))))))
✓	32.0b	(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
✓	31.2b	(log.f64 (/.f64 (+.f64 N 1) N))
✓	29.7b	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N))))
	45.6b	(fma.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 2)) (cbrt.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))) (*.f64 1/3 (pow.f64 N -3)))

Compiler

Compiled 3361 to 2250 computations (33.1% saved)

regimes49.0ms (1.8%)

Accuracy

Total -63.6b remaining (-227230%)

Threshold costs -63.6b (-227230%)

Counts

26 → 2

Calls

Call 1

Inputs
(+.f64 (/.f64 1 N) 0)
(+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N))))
(fma.f64 (cbrt.f64 (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 2)) (cbrt.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N))))) (*.f64 1/3 (pow.f64 N -3)))
(/.f64 (+.f64 (.f64 1/27 (pow.f64 (pow.f64 N -3) 3)) (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 3)) (+.f64 (/.f64 1/9 (pow.f64 N 6)) (-.f64 (pow.f64 (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (.f64 N N)))) 2) (.f64 (.f64 1/3 (pow.f64 N -3)) (+.f64 (pow.f64 N -1) (-.f64 (.f64 -1/4 (pow.f64 N -4)) (/.f64 1/2 (*.f64 N N))))))))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 1 N) (/.f64 1/2 (*.f64 N N))))
(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (*.f64 N N)) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))))
(fma.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log1p.f64 N)) (neg.f64 (log.f64 N)))
(log.f64 (/.f64 (+.f64 N 1) N))
(pow.f64 (cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 3)
(*.f64 (+.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))) (-.f64 (sqrt.f64 (log1p.f64 N)) (sqrt.f64 (log.f64 N))))
(*.f64 (cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) (pow.f64 (cbrt.f64 (-.f64 (log1p.f64 N) (log.f64 N))) 2))
(+.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)))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 1 N) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N))))
(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
(+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.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 1 N) (/.f64 (/.f64 1/2 N) N))
(-.f64 (/.f64 1 N) (*.f64 1/2 (/.f64 1 (pow.f64 N 2))))
(/.f64 1 N)
(-.f64 N (log.f64 N))
(+.f64 N (*.f64 -1 (log.f64 N)))
(neg.f64 (log.f64 N))
(*.f64 -1 (log.f64 N))
(-.f64 (log1p.f64 N) (log.f64 N))
(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

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

Results

24.0ms	0.0b	`N`
15.0ms	0.0b	`(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))`

Compiler

Compiled 397 to 257 computations (35.3% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

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

Steps

Iters	Point		Range
0.0001	∈ [	5.3092036123914e-5	,	0.00821953553258048	]

Compiler

Compiled 12 to 9 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	56
1	37	56
2	46	56
3	55	56
4	59	56
5	60	56

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 7378697629483821/73786976294838206464) (+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N)))) (log.f64 (/.f64 (+.f64 N 1) N)))

Outputs

(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 7378697629483821/73786976294838206464) (+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (-.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 1/2 N) N)))) (log.f64 (/.f64 (+.f64 N 1) N)))

(if (<=.f64 (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) 7378697629483821/73786976294838206464) (+.f64 (/.f64 1 N) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (+.f64 (/.f64 -1/4 (pow.f64 N 4)) (/.f64 (/.f64 -1/2 N) N)))) (log.f64 (/.f64 (+.f64 N 1) N)))

end28.0ms (1%)

Stop Event

1×

fuel

Compiler

Compiled 76 to 58 computations (23.7% saved)

Details

analyze3.0ms (0.1%)

sample2.0s (75.3%)

preprocess18.0ms (0.7%)

simplify9.0ms (0.3%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series2.0ms (0.1%)

rewrite37.0ms (1.4%)

simplify23.0ms (0.9%)

prune33.0ms (1.2%)

localize15.0ms (0.6%)

series6.0ms (0.2%)

rewrite39.0ms (1.5%)

simplify22.0ms (0.8%)

prune99.0ms (3.7%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite38.0ms (1.4%)

simplify23.0ms (0.9%)

prune38.0ms (1.4%)

localize7.0ms (0.3%)

series9.0ms (0.3%)

rewrite32.0ms (1.2%)

simplify33.0ms (1.2%)

prune77.0ms (2.9%)

regimes49.0ms (1.8%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end28.0ms (1%)

Profiling