Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample1.7s (77.2%)

Results

795.0ms	2090×	body	1024	valid
425.0ms	4409×	body	128	valid
273.0ms	1031×	body	512	valid
97.0ms	216×	body	2048	valid
92.0ms	510×	body	256	valid

Compiler

Compiled 26 to 24 computations (7.7% saved)

preprocess37.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

868×	`unswap-sqr_binary64`
380×	`associate-l_binary64`
316×	`associate-/l/_binary64`
260×	`associate-r_binary64`
252×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	30
1	29	30
2	41	30
3	58	30
4	103	30
5	226	30
6	602	30
7	1879	30
8	4934	30
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 12 to 11 computations (8.3% saved)

simplify28.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

978×	`times-frac_binary64`
434×	`unswap-sqr_binary64`
374×	`associate-*l/_binary64`
342×	`associate-/l*_binary64`
228×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	19	15
2	25	15
3	34	15
4	59	15
5	124	15
6	311	15
7	972	15
8	2549	15
9	4189	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

31.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.0b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

Compiler

Compiled 46 to 42 computations (8.7% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 (*.f64 -2 x)))
✓	0.0b	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))
✓	2.9b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

series19.0ms (0.9%)

Counts

3 → 20

Calls

9 calls:

6.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))	x	inf
3.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)	x	-inf
3.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)	x	inf
3.0ms	(/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x))))	x	-inf
1.0ms	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)	x	0

rewrite55.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

426×	`log-prod_binary64`
259×	`prod-diff_binary64`
227×	`fma-def_binary64`
175×	`expm1-udef_binary64`
175×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	217	36
2	2712	36

Stop Event

1×	node limit

Counts

3 → 114

simplify33.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-def_binary64`
431×	`distribute-rgt-neg-in_binary64`
352×	`distribute-lft-neg-in_binary64`
349×	`cancel-sign-sub-inv_binary64`
277×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	257
1	126	252
2	325	238
3	1082	231
4	3632	231

Stop Event

1×	node limit

Counts

134 → 136

prune75.0ms (3.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	135	2	137

Error

Counts

137 → 2

Alt Table

Status	Error	Program
▶	30.6b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	31.0b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

Compiler

Compiled 2289 to 1889 computations (17.5% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 3) -1/3 x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

1.0ms	(fma.f64 (pow.f64 x 3) -1/3 x)	x	-inf
1.0ms	(fma.f64 (pow.f64 x 3) -1/3 x)	x	inf
1.0ms	(fma.f64 (pow.f64 x 3) -1/3 x)	x	0

rewrite28.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

522×	`pow1_binary64`
492×	`add-log-exp_binary64`
492×	`log1p-expm1-u_binary64`
492×	`expm1-log1p-u_binary64`
482×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	130	8
2	1341	8

Stop Event

1×	node limit

Counts

1 → 21

simplify28.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1047×	`fma-def_binary64`
818×	`unswap-sqr_binary64`
241×	`associate-l_binary64`
194×	`fma-neg_binary64`
174×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	105
1	23	105
2	61	87
3	194	87
4	429	87
5	1190	87
6	2374	87
7	3266	87

Stop Event

1×	node limit

Counts

33 → 26

prune10.0ms (0.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	26	2	28

Error

Counts

28 → 2

Alt Table

Status	Error	Program
✓	30.6b	(fma.f64 (pow.f64 x 3) -1/3 x)
✓	31.0b	(-.f64 (/.f64 2 (+.f64 1 (exp.f64 (*.f64 -2 x)))) 1)

Compiler

Compiled 288 to 219 computations (24% saved)

regimes109.0ms (5%)

Accuracy

Total 0.4b remaining (95%)

Threshold costs 0.4b (95%)

Counts

7 → 3

Compiler

Compiled 542 to 465 computations (14.2% saved)

bsearch0.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms	(*.f64 -2 x)
0.0ms	(*.f64 -2 x)

Steps

Iters	Point		Range
2.7684265819523093e-10	∈ [	2.7684265819523093e-10	,	200679462527.09012	]
-1075030.39031869	∈ [	-1075030.39031869	,	-0.0001510867242417076	]

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	56
1	25	56
2	30	56
3	32	56
4	33	56

Stop Event

1×

saturated

end57.0ms (2.6%)

Stop Event

1×

done

Compiler

Compiled 96 to 79 computations (17.7% saved)

Details

analyze1.0ms (0.1%)

sample1.7s (77.2%)

preprocess37.0ms (1.7%)

simplify28.0ms (1.3%)

prune2.0ms (0.1%)

localize6.0ms (0.3%)

series19.0ms (0.9%)

rewrite55.0ms (2.5%)

simplify33.0ms (1.5%)

prune75.0ms (3.4%)

localize3.0ms (0.2%)

series3.0ms (0.1%)

rewrite28.0ms (1.3%)

simplify28.0ms (1.3%)

prune10.0ms (0.5%)

regimes109.0ms (5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end57.0ms (2.6%)

Profiling