Details

analyze764.0ms (15.1%)

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)

sample3.3s (65.2%)

Results

1.6s	8256×	body	128	valid
1.5s	8309×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify175.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-neg_binary64`
804×	`unsub-neg_binary64`
461×	`distribute-neg-in_binary64`
434×	`sub-neg_binary64`
338×	`distribute-rgt-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	64	12
5	113	12
6	247	12
7	500	12
8	1560	12
9	2513	12
10	3218	12
11	3602	12
12	3803	12
13	3974	12
14	4075	12
15	4392	12
16	4836	12
17	4898	12
18	4901	12

prune5.0ms (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

32.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.3b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓	30.0b	(sqrt.f64 (fma.f64 x x -1))

series25.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

12.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
7.0ms	(sqrt.f64 (fma.f64 x x -1))
6.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`
5×	`pow1_binary64`

Counts

3 → 49

Calls

3 calls:

6.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
6.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
2.0ms	(sqrt.f64 (fma.f64 x x -1))

simplify120.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
330×	`sub-neg_binary64`
301×	`fma-def_binary64`
254×	`distribute-neg-frac_binary64`
210×	`associate-+l+_binary64`

Counts

85 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	1395
1	401	1305
2	1052	1265
3	3424	1265
4	4773	1265
5	4915	1265

prune122.0ms (2.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	2	119

Error

Counts

119 → 2

Alt Table

Status	Error	Program
	32.3b	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))
▶	0.1b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 1903 to 1421 computations (25.3% saved)

localize10.0ms (0.2%)

prune3.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

Counts

2 → 2

Alt Table

Status	Error	Program
▶	32.3b	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))
✓	0.1b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))
✓	0.0b	(+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1)))))
✓	5.8b	(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))
	30.0b	(sqrt.f64 (fma.f64 x x -1))

series25.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

11.0ms	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))
7.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))
6.0ms	(+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1)))))

rewrite15.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`
4×	`log-prod_binary64`

Counts

3 → 46

Calls

3 calls:

6.0ms	(+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1)))))
4.0ms	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))
1.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))

simplify127.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

580×	`fma-neg_binary64`
333×	`sub-neg_binary64`
297×	`fma-def_binary64`
254×	`distribute-neg-frac_binary64`
206×	`associate-+l+_binary64`

Counts

82 → 136

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	157	1433
1	398	1295
2	1033	1291
3	3407	1245
4	4754	1245
5	4900	1245

prune174.0ms (3.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	174	0	174
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	174	2	176

Error

Counts

176 → 2

Alt Table

Status	Error	Program
✓	32.3b	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))
✓	0.1b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 2902 to 2206 computations (24% saved)

regimes61.0ms (1.2%)

Accuracy

Total 0.3b remaining (84.1%)

Threshold costs 0.3b (84.1%)

Counts

10 → 1

Compiler

Compiled 258 to 187 computations (27.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	7	10

end85.0ms (1.7%)

Compiler: Compiled 35 to 26 computations (25.7% saved)

Details

analyze764.0ms (15.1%)

sample3.3s (65.2%)

simplify175.0ms (3.5%)

prune5.0ms (0.1%)

localize13.0ms (0.3%)

series25.0ms (0.5%)

rewrite16.0ms (0.3%)

simplify120.0ms (2.4%)

prune122.0ms (2.4%)

localize10.0ms (0.2%)

prune3.0ms (0.1%)

localize20.0ms (0.4%)

series25.0ms (0.5%)

rewrite15.0ms (0.3%)

simplify127.0ms (2.5%)

prune174.0ms (3.4%)

regimes61.0ms (1.2%)

simplify4.0ms (0.1%)

end85.0ms (1.7%)

Profiling