Details

analyze391.0ms (15.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.7s (68.7%)

Results

863.0ms	8256×	body	128	valid
807.0ms	8327×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify28.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-neg_binary64`
396×	`unsub-neg_binary64`
348×	`distribute-neg-in_binary64`
330×	`fma-def_binary64`
262×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	78	12
5	154	12
6	360	12
7	751	12
8	2365	12
9	4284	12

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

36.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	36.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 38 to 26 computations (31.6% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
✓	0.0b	(-.f64 (*.f64 x x) 1)
✓	0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
✓	33.9b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

series13.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

5.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
3.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))
3.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
2.0ms	(-.f64 (*.f64 x x) 1)

rewrite50.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

831×	`log1p-expm1-u_binary64`
831×	`expm1-log1p-u_binary64`
124×	`egg-rr`
85×	`add-sqr-sqrt_binary64`
83×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	34
1	176	34
2	2396	34

Stop Event

1×	node limit

Counts

4 → 124

Calls

4 calls:

48.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
48.0ms	(-.f64 (*.f64 x x) 1)
48.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
48.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify38.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

448×	`fma-neg_binary64`
304×	`sub-neg_binary64`
256×	`distribute-neg-frac_binary64`
231×	`fma-def_binary64`
184×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	105	753
1	310	702
2	929	700
3	3405	700

Stop Event

1×	node limit

Counts

172 → 191

prune96.0ms (3.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	190	2	192

Error

Counts

192 → 2

Alt Table

Status	Error	Program
✓	36.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 2847 to 2095 computations (26.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

rewrite36.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
283×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	146	10
2	1652	10

Stop Event

1×	node limit

Counts

1 → 26

Calls

1 calls:

35.0ms

(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

simplify26.0ms (1%)

Algorithm

1×	egg-herbie

Rules

729×	`fma-def_binary64`
409×	`cancel-sign-sub-inv_binary64`
350×	`sub-neg_binary64`
309×	`fma-neg_binary64`
240×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	59	272
1	162	258
2	510	258
3	1988	258

Stop Event

1×	node limit

Counts

38 → 48

prune25.0ms (1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	48	2	50

Error

Counts

50 → 2

Alt Table

Status	Error	Program
✓	36.2b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
✓	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 728 to 565 computations (22.4% saved)

regimes30.0ms (1.2%)

Accuracy

Total 0.3b remaining (81.7%)

Threshold costs 0.3b (81.7%)

Counts

10 → 1

Compiler

Compiled 249 to 181 computations (27.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10

Stop Event

1×

saturated

end40.0ms (1.6%)

Compiler: Compiled 34 to 25 computations (26.5% saved)

Details

analyze391.0ms (15.5%)

sample1.7s (68.7%)

simplify28.0ms (1.1%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series13.0ms (0.5%)

rewrite50.0ms (2%)

simplify38.0ms (1.5%)

prune96.0ms (3.8%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite36.0ms (1.4%)

simplify26.0ms (1%)

prune25.0ms (1%)

regimes30.0ms (1.2%)

simplify2.0ms (0.1%)

end40.0ms (1.6%)

Profiling