Details

analyze2.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample38.0ms (6.9%)

Algorithm

1×

intervals

Results

16.0ms	57×	body	1280	valid
8.0ms	42×	body	640	valid
7.0ms	134×	body	80	valid
2.0ms	15×	body	320	valid
1.0ms	8×	body	160	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify16.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune7.0ms (1.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 28.7b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (1.1%)

Local error

Found 2 expressions with local error:

2.4b	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
2.8b	(log.f64 (+.f64 N 1))

rewrite12.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
11×	`log-prod_binary64`
7×	`pow1_binary64` `add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64` `log-pow_binary64`
4×	`distribute-lft-out--_binary64` `log-div_binary64` `associate--l+_binary64`
3×	`associate--r+_binary64` `add-exp-log_binary64`
2×	`flip3-+_binary64` `add-log-exp_binary64` `associate--l-_binary64` `distribute-lft-out_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `difference-of-squares_binary64` `flip--_binary64`

Counts

2 → 40

Calls

2 calls:

7.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
4.0ms	(log.f64 (+.f64 N 1))

series9.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

5.0ms	(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))
4.0ms	(log.f64 (+.f64 N 1))

simplify67.0ms (12.2%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5079	648

prune44.0ms (8.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	2	47

Merged error: 0.1b

Counts

47 → 2

Compiler

Compiled 611 to 401 computations (34.4% saved)

localize5.0ms (0.8%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 N 1) N)
2.3b	(log.f64 (/.f64 (+.f64 N 1) N))

rewrite12.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
16×	`log-prod_binary64`
7×	`distribute-lft-out_binary64` `add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `associate-/l*_binary64`
3×	`associate-/r*_binary64` `pow1_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `rem-log-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64`

Counts

2 → 60

Calls

2 calls:

6.0ms	(/.f64 (+.f64 N 1) N)
5.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

series9.0ms (1.7%)

Counts

2 → 6

Calls

2 calls:

5.0ms	(/.f64 (+.f64 N 1) N)
4.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

simplify118.0ms (21.5%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5093	940

prune38.0ms (7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	64	4	68

Merged error: 0.0b

Counts

68 → 4

Compiler

Compiled 823 to 558 computations (32.2% saved)

localize9.0ms (1.7%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (/.f64 (+.f64 N 1) N))
0.0b	(sqrt.f64 (/.f64 (+.f64 N 1) N))
2.3b	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
2.3b	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))

rewrite26.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`sqrt-prod_binary64`
62×	`*-un-lft-identity_binary64`
50×	`times-frac_binary64`
44×	`add-sqr-sqrt_binary64`
38×	`log-prod_binary64` `add-cube-cbrt_binary64`
12×	`distribute-lft-out_binary64`
10×	`pow1_binary64`
6×	`log-pow_binary64` `add-exp-log_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `sqrt-div_binary64`
2×	`rem-log-exp_binary64` `log-div_binary64`

Counts

4 → 118

Calls

4 calls:

6.0ms	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
6.0ms	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
5.0ms	(sqrt.f64 (/.f64 (+.f64 N 1) N))
5.0ms	(sqrt.f64 (/.f64 (+.f64 N 1) N))

series21.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

7.0ms	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
6.0ms	(log.f64 (sqrt.f64 (/.f64 (+.f64 N 1) N)))
4.0ms	(sqrt.f64 (/.f64 (+.f64 N 1) N))
4.0ms	(sqrt.f64 (/.f64 (+.f64 N 1) N))

simplify89.0ms (16.3%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4930	2350
1	4930	2350

Details

analyze2.0ms (0.3%)

sample38.0ms (6.9%)

simplify16.0ms (2.9%)

prune7.0ms (1.3%)

localize6.0ms (1.1%)

rewrite12.0ms (2.1%)

series9.0ms (1.6%)

simplify67.0ms (12.2%)

prune44.0ms (8.1%)

localize5.0ms (0.8%)

rewrite12.0ms (2.3%)

series9.0ms (1.7%)

simplify118.0ms (21.5%)

prune38.0ms (7%)

localize9.0ms (1.7%)

rewrite26.0ms (4.7%)

series21.0ms (3.9%)

simplify89.0ms (16.3%)

prune19.0ms (3.4%)

Profiling