Details

analyze420.0ms (7.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample4.4s (82.7%)

Results

1.8s	2713×	body	1024	valid
1.5s	1168×	body	2048	valid
538.0ms	1305×	body	512	valid
284.0ms	2383×	body	128	valid
147.0ms	648×	body	256	valid
31.0ms	39×	body	4096	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify67.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`hypot-1-def_binary64`
1×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	13	9
2	14	9
3	13	9

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

45.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	45.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize4.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 x)
✓	0.7b	(+.f64 x (hypot.f64 1 x))
✓	4.2b	(log.f64 (+.f64 x (hypot.f64 1 x)))

series13.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(+.f64 x (hypot.f64 1 x))
4.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
3.0ms	(hypot.f64 1 x)

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-exp-log_binary64`

Counts

3 → 44

Calls

3 calls:

2.0ms	(log.f64 (+.f64 x (hypot.f64 1 x)))
2.0ms	(+.f64 x (hypot.f64 1 x))
0.0ms	(hypot.f64 1 x)

simplify78.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
469×	`cancel-sign-sub-inv_binary64`
426×	`associate-/r*_binary64`
376×	`fma-def_binary64`
361×	`sub-neg_binary64`

Counts

80 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	1089
1	394	1025
2	959	1013
3	2675	1013
4	4999	1013
5	5338	1013

prune59.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	3	114

Error

Counts

114 → 3

Alt Table

Status	Error	Program
▶	29.1b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
	49.2b	(log.f64 (/.f64 -1/2 x))
✓	45.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 1561 to 1174 computations (24.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 3/40 (pow.f64 x 5) x)
✓	17.7b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))

series10.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(fma.f64 3/40 (pow.f64 x 5) x)
4.0ms	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
0.0ms	(fma.f64 3/40 (pow.f64 x 5) x)

simplify52.0ms (1%)

Algorithm

1×	egg-herbie

Rules

612×	`associate-l_binary64`
578×	`associate-r_binary64`
480×	`distribute-lft-in_binary64`
480×	`distribute-rgt-in_binary64`
291×	`fma-def_binary64`

Counts

44 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	584
1	65	520
2	153	518
3	599	518
4	3541	518
5	4941	518

prune18.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	31	3	34

Error

Counts

34 → 3

Alt Table

Status	Error	Program
✓	29.1b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
▶	49.2b	(log.f64 (/.f64 -1/2 x))
✓	45.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 486 to 369 computations (24.1% saved)

localize3.0ms (0.1%)

prune2.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	29.1b	(fma.f64 (pow.f64 x 3) -1/6 (fma.f64 3/40 (pow.f64 x 5) x))
✓	49.2b	(log.f64 (/.f64 -1/2 x))
✓	45.8b	(log.f64 (+.f64 x (hypot.f64 1 x)))

Compiler

Compiled 24 to 18 computations (25% saved)

regimes57.0ms (1.1%)

Accuracy

Total 0.1b remaining (53.1%)

Threshold costs 0.1b (53.1%)

Counts

12 → 3

Compiler

Compiled 309 to 232 computations (24.9% saved)

bsearch47.0ms (0.9%)

Steps

Iters	Range		Point
10	3.08042433273409e-8	805269.0388429543	0.008183541869942034
10	-770347622.350186	-0.0001958338778048188	-1.3291109624821573

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	46
1	38	46
2	45	46
3	49	46
4	52	46
5	53	46
6	51	46

end66.0ms (1.2%)

Compiler: Compiled 88 to 66 computations (25% saved)

Details

analyze420.0ms (7.9%)

sample4.4s (82.7%)

simplify67.0ms (1.3%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series13.0ms (0.3%)

rewrite7.0ms (0.1%)

simplify78.0ms (1.5%)

prune59.0ms (1.1%)

localize6.0ms (0.1%)

series10.0ms (0.2%)

rewrite1.0ms (0%)

simplify52.0ms (1%)

prune18.0ms (0.3%)

localize3.0ms (0.1%)

prune2.0ms (0%)

regimes57.0ms (1.1%)

bsearch47.0ms (0.9%)

simplify4.0ms (0.1%)

end66.0ms (1.2%)

Profiling