Details

analyze469.0ms (17.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	81.1%	18.9%	7
6.2%	74.9%	18.9%	8
9.4%	65.5%	25.1%	9
15.6%	48.4%	36%	10
20.3%	43.1%	36.6%	11
22.6%	36%	41.4%	12
27.1%	25.1%	47.8%	13
29.5%	22.5%	48%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (44.2%)

Results

888.0ms	8256×	body	128	valid
259.0ms	2630×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify29.0ms (1%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-def_binary64`
584×	`fma-neg_binary64`
283×	`distribute-rgt-in_binary64`
228×	`sub-neg_binary64`
220×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	19	15
2	31	15
3	60	15
4	134	15
5	383	15
6	833	15
7	1633	15
8	3632	15

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

26.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	26.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 49 to 29 computations (40.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	1.8b	(-.f64 (.f64 y y) (.f64 z z))
✓	25.6b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series19.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
7.0ms	(-.f64 (.f64 y y) (.f64 z z))

rewrite63.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

757×	`log1p-expm1-u_binary64`
757×	`expm1-log1p-u_binary64`
642×	`prod-diff_binary64`
148×	`egg-rr`
78×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	22
1	159	22
2	2172	22

Stop Event

1×	node limit

Counts

2 → 148

Calls

2 calls:

60.0ms	(-.f64 (.f64 y y) (.f64 z z))
60.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

simplify56.0ms (2%)

Algorithm

1×	egg-herbie

Rules

685×	`times-frac_binary64`
310×	`associate-/l*_binary64`
292×	`associate-/r*_binary64`
197×	`associate-r_binary64`
177×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	73	872
1	233	864
2	800	848
3	4891	848

Stop Event

1×	node limit

Counts

196 → 193

prune100.0ms (3.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	190	3	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	191	3	194

Error

0.1b

Counts

194 → 3

Alt Table

Status	Error	Program
	35.5b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
▶	26.9b	(.f64 x (fma.f64 1/2 (.f64 (/.f64 z y) z) (neg.f64 y)))
	33.8b	(.f64 x (fma.f64 (.f64 (/.f64 z y) z) -1/2 y))

Compiler

Compiled 4590 to 1866 computations (59.3% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 z y) z)

series9.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(*.f64 (/.f64 z y) z)

rewrite37.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

525×	`log1p-expm1-u_binary64`
525×	`expm1-log1p-u_binary64`
412×	`unpow-prod-down_binary64`
294×	`log-prod_binary64`
143×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	105	7
2	1422	7

Stop Event

1×	node limit

Counts

1 → 27

Calls

1 calls:

36.0ms

(*.f64 (/.f64 z y) z)

simplify51.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

434×	`unswap-sqr_binary64`
423×	`associate-*r/_binary64`
395×	`associate-/r/_binary64`
392×	`associate-/r*_binary64`
333×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	11	168
2	20	168
3	37	168
4	83	168
5	256	168
6	1053	168
7	3447	168
8	4249	168
9	4434	168
10	4650	168
11	4981	168

Stop Event

1×	node limit

Counts

51 → 29

prune14.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	29	3	32

Error

0.1b

Counts

32 → 3

Alt Table

Status	Error	Program
	35.5b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
✓	26.9b	(.f64 x (fma.f64 1/2 (.f64 (/.f64 z y) z) (neg.f64 y)))
▶	33.8b	(.f64 x (fma.f64 (.f64 (/.f64 z y) z) -1/2 y))

Compiler

Compiled 480 to 217 computations (54.8% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.1b	(*.f64 (/.f64 z y) z)

prune15.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	29	3	32

Error

0.1b

Counts

32 → 3

Alt Table

Status	Error	Program
▶	35.5b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
✓	26.9b	(.f64 x (fma.f64 1/2 (.f64 (/.f64 z y) z) (neg.f64 y)))
✓	33.8b	(.f64 x (fma.f64 (.f64 (/.f64 z y) z) -1/2 y))

Compiler

Compiled 438 to 209 computations (52.3% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 y z))
✓	0.2b	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))

series29.0ms (1.1%)

Counts

2 → 28

Calls

2 calls:

17.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))
12.0ms	(sqrt.f64 (+.f64 y z))

rewrite51.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

868×	`expm1-log1p-u_binary64`
534×	`prod-diff_binary64`
86×	`add-sqr-sqrt_binary64`
83×	`log1p-expm1-u_binary64`
82×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	175	18
2	2393	18

Stop Event

1×	node limit

Counts

2 → 43

Calls

2 calls:

50.0ms	(sqrt.f64 (+.f64 y z))
50.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))

simplify30.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

685×	`times-frac_binary64`
320×	`fma-def_binary64`
314×	`associate-/r*_binary64`
307×	`associate-/l*_binary64`
290×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	805
1	310	789
2	1052	761

Stop Event

1×	node limit

Counts

71 → 88

prune43.0ms (1.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	88	3	91

Error

0.1b

Counts

91 → 3

Alt Table

Status	Error	Program
✓	35.5b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
✓	26.9b	(.f64 x (fma.f64 1/2 (.f64 (/.f64 z y) z) (neg.f64 y)))
✓	33.8b	(.f64 x (fma.f64 (.f64 (/.f64 z y) z) -1/2 y))

Compiler

Compiled 1769 to 978 computations (44.7% saved)

regimes369.0ms (13.5%)

Accuracy

Total 0.2b remaining (58.7%)

Threshold costs 0.2b (58.7%)

Counts

19 → 2

Compiler

Compiled 1973 to 1342 computations (32% saved)

bsearch54.0ms (2%)

Steps

Iters	Range		Point
2	-7.720718528621749e-259	1.3481547609359637e-298	-8.509366001875281e-289

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	36
1	24	36
2	26	36
3	27	36

Stop Event

1×

saturated

end56.0ms (2.1%)

Compiler: Compiled 97 to 56 computations (42.3% saved)

Details

analyze469.0ms (17.2%)

sample1.2s (44.2%)

simplify29.0ms (1%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series19.0ms (0.7%)

rewrite63.0ms (2.3%)

simplify56.0ms (2%)

prune100.0ms (3.7%)

localize7.0ms (0.2%)

series9.0ms (0.3%)

rewrite37.0ms (1.3%)

simplify51.0ms (1.9%)

prune14.0ms (0.5%)

localize6.0ms (0.2%)

prune15.0ms (0.5%)

localize7.0ms (0.3%)

series29.0ms (1.1%)

rewrite51.0ms (1.9%)

simplify30.0ms (1.1%)

prune43.0ms (1.6%)

regimes369.0ms (13.5%)

bsearch54.0ms (2%)

simplify3.0ms (0.1%)

end56.0ms (2.1%)

Profiling