Details

analyze46.0ms (3%)

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
50%	50%	0.1%	6
68.7%	31.2%	0.1%	7
81.2%	18.7%	0.1%	8
89%	10.9%	0.1%	9
92.1%	7.8%	0.1%	10
95.6%	4.3%	0.1%	11
96.4%	3.5%	0.1%	12
98%	1.9%	0.1%	13
98.2%	1.7%	0.1%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample786.0ms (52%)

Results

741.0ms

8256×

body

128

valid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify20.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

546×	`times-frac_binary64`
408×	`fma-def_binary64`
310×	`div-sub_binary64`
277×	`associate-/l*_binary64`
265×	`associate-/r*_binary64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	16	13
2	41	13
3	87	13
4	178	13
5	356	13
6	652	11
7	1398	11

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.9b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))
	16.3b	(/.f64 (.f64 (.f64 x 2) y) (-.f64 x y))

Compiler

Compiled 61 to 40 computations (34.4% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.9b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

series9.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

9.0ms

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

rewrite39.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

809×	`log1p-expm1-u_binary64`
809×	`expm1-log1p-u_binary64`
84×	`add-sqr-sqrt_binary64`
79×	`add-log-exp_binary64`
78×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	171	11
2	2158	11

Stop Event

1×	node limit

Counts

1 → 33

Calls

1 calls:

39.0ms

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

simplify30.0ms (2%)

Algorithm

1×	egg-herbie

Rules

411×	`fma-neg_binary64`
367×	`cancel-sign-sub-inv_binary64`
294×	`associate-/l/_binary64`
277×	`associate-/r/_binary64`
216×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	510
1	134	492
2	469	444
3	1988	432

Stop Event

1×	node limit

Counts

57 → 47

prune27.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	45	4	49

Error

Counts

49 → 4

Alt Table

Status	Error	Program
	35.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))))
	32.0b	(*.f64 2 y)
▶	30.9b	(.f64 -2 (+.f64 x (.f64 x (*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x y)))))
✓	5.9b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

Compiler

Compiled 774 to 491 computations (36.6% saved)

localize7.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x y)))
✓	0.1b	(*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x y))

series29.0ms (1.9%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(.f64 x (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x y)))
12.0ms	(*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x y))

rewrite52.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

896×	`log1p-expm1-u_binary64`
896×	`expm1-log1p-u_binary64`
250×	`prod-diff_binary64`
86×	`add-sqr-sqrt_binary64`
80×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	29
1	172	29
2	2424	29

Stop Event

1×	node limit

Counts

2 → 62

Calls

2 calls:

50.0ms	(.f64 x (.f64 (+.f64 (/.f64 x y) 1) (/.f64 x y)))
50.0ms	(*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x y))

simplify27.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

551×	`associate-/l/_binary64`
548×	`associate-/r*_binary64`
433×	`associate-*l/_binary64`
423×	`associate-l_binary64`
392×	`associate-/r/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	723
1	31	723
2	63	615
3	183	615
4	918	543

Stop Event

1×	node limit

Counts

110 → 73

prune41.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	73	4	77

Error

Counts

77 → 4

Alt Table

Status	Error	Program
	35.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))))
▶	32.0b	(*.f64 2 y)
✓	30.9b	(.f64 -2 (+.f64 x (.f64 x (*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x y)))))
✓	5.9b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

Compiler

Compiled 1444 to 762 computations (47.2% saved)

localize2.0ms (0.1%)

prune7.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

Counts

4 → 4

Alt Table

Status	Error	Program
▶	35.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))))
✓	32.0b	(*.f64 2 y)
✓	30.9b	(.f64 -2 (+.f64 x (.f64 x (*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x y)))))
✓	5.9b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

Compiler

Compiled 64 to 43 computations (32.8% saved)

localize8.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))
✓	0.9b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))))
✓	1.8b	(*.f64 (sqrt.f64 x) (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)))

series45.0ms (2.9%)

Counts

3 → 56

Calls

3 calls:

24.0ms	(*.f64 (sqrt.f64 x) (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)))
13.0ms	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))))
8.0ms	(/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))

rewrite49.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

562×	`log-prod_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
182×	`log-pow_binary64`
116×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	38
1	248	35
2	2967	35

Stop Event

1×	node limit

Counts

3 → 76

Calls

3 calls:

47.0ms	(/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))
47.0ms	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))))
47.0ms	(*.f64 (sqrt.f64 x) (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2)))

simplify35.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

757×	`fma-def_binary64`
332×	`times-frac_binary64`
221×	`associate-/l*_binary64`
220×	`associate-/r*_binary64`
199×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1361
1	369	1272
2	1295	1116

Stop Event

1×	node limit

Counts

132 → 121

prune61.0ms (4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	121	4	125

Error

Counts

125 → 4

Alt Table

Status	Error	Program
✓	35.6b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (/.f64 1 (fma.f64 1/2 (/.f64 x y) -1/2))))
✓	32.0b	(*.f64 2 y)
✓	30.9b	(.f64 -2 (+.f64 x (.f64 x (*.f64 (+.f64 (/.f64 x y) 1) (/.f64 x y)))))
✓	5.9b	(/.f64 x (fma.f64 1/2 (/.f64 x y) -1/2))

Compiler

Compiled 2265 to 1378 computations (39.2% saved)

regimes105.0ms (7%)

Accuracy

Total 0.6b remaining (98.6%)

Threshold costs 0.6b (98.6%)

Counts

16 → 5

Compiler

Compiled 577 to 385 computations (33.3% saved)

bsearch1.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

3×	`*-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	26	131
1	30	131
2	34	131
3	36	131
4	37	131

Stop Event

1×

saturated

end76.0ms (5%)

Compiler: Compiled 232 to 136 computations (41.4% saved)

Details

analyze46.0ms (3%)

sample786.0ms (52%)

simplify20.0ms (1.3%)

prune3.0ms (0.2%)

localize5.0ms (0.3%)

series9.0ms (0.6%)

rewrite39.0ms (2.6%)

simplify30.0ms (2%)

prune27.0ms (1.8%)

localize7.0ms (0.5%)

series29.0ms (1.9%)

rewrite52.0ms (3.4%)

simplify27.0ms (1.8%)

prune41.0ms (2.7%)

localize2.0ms (0.1%)

prune7.0ms (0.5%)

localize8.0ms (0.5%)

series45.0ms (2.9%)

rewrite49.0ms (3.2%)

simplify35.0ms (2.3%)

prune61.0ms (4%)

regimes105.0ms (7%)

bsearch1.0ms (0%)

simplify4.0ms (0.3%)

end76.0ms (5%)

Profiling