Details

analyze1.1s (28.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 24 to 18 computations (25% saved)

sample50.0ms (1.3%)

Algorithm

1×

intervals

Results

14.0ms	199×	body	128	valid
6.0ms	18×	body	2048	valid
5.0ms	256×	pre	128	true
5.0ms	11×	body	4096	valid
3.0ms	12×	body	1024	valid
2.0ms	9×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 45 to 34 computations (24.4% saved)

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	31	24
2	39	22
3	45	22
4	47	22
5	49	22
6	50	22
7	47	22

prune16.0ms (0.4%)

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

11.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))

Compiler

Compiled 68 to 48 computations (29.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
✓	0.0b	(fma.f64 x x (.f64 p (.f64 4 p)))
✓	0.5b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
✓	16.6b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
15×	`sqrt-prod_binary64`

Counts

4 → 76

Calls

4 calls:

3.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
1.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))
0.0ms	(fma.f64 x x (.f64 p (.f64 4 p)))
0.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)

series99.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

29.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
28.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
25.0ms	(fma.f64 x x (.f64 p (.f64 4 p)))
16.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

simplify139.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-neg_binary64`
671×	`times-frac_binary64`
400×	`associate-/l*_binary64`
398×	`fma-def_binary64`
332×	`associate-/r*_binary64`

Counts

172 → 319

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	215	3678
1	550	3488
2	1578	3438
3	4760	3438
4	5199	3438

prune177.0ms (4.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	316	3	319
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	316	4	320

Error

4.2b

Counts

320 → 4

Alt Table

Status	Error	Program
▶	52.2b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
	53.3b	(sqrt.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
✓	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	56.8b	(sqrt.f64 (fma.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6)) (fma.f64 (/.f64 p x) (/.f64 p x) (fma.f64 (/.f64 (pow.f64 p 8) (pow.f64 x 8)) -35 (*.f64 (/.f64 (pow.f64 p 4) (pow.f64 x 4)) -3)))))

Compiler

Compiled 5027 to 3355 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 p (/.f64 (*.f64 x x) p))
✓	0.2b	(/.f64 (*.f64 x x) p)
✓	24.2b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`times-frac_binary64`
40×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
35×	`add-cube-cbrt_binary64`
26×	`sqrt-prod_binary64`

Counts

3 → 114

Calls

3 calls:

5.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
5.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
5.0ms	(/.f64 (*.f64 x x) p)

series102.0ms (2.6%)

Counts

3 → 72

Calls

3 calls:

53.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
29.0ms	(/.f64 (*.f64 x x) p)
20.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

simplify165.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

676×	`times-frac_binary64`
393×	`associate-/l*_binary64`
381×	`associate-/l/_binary64`
365×	`unswap-sqr_binary64`
334×	`fma-neg_binary64`

Counts

186 → 338

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	170	2504
1	300	2325
2	853	2121
3	3029	2022
4	4200	1918
5	4963	1918
6	4993	1918

prune58.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	336	2	338
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	339	3	342

Error

Counts

342 → 3

Alt Table

Status	Error	Program
	55.2b	(neg.f64 (/.f64 p x))
▶	53.0b	(/.f64 p x)
✓	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))

Compiler

Compiled 2747 to 769 computations (72% saved)

localize2.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
▶	55.2b	(neg.f64 (/.f64 p x))
✓	53.0b	(/.f64 p x)
✓	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))

Compiler

Compiled 34 to 23 computations (32.4% saved)

localize5.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune2.0ms (0.1%)

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
✓	55.2b	(neg.f64 (/.f64 p x))
✓	53.0b	(/.f64 p x)
✓	11.6b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))

Compiler

Compiled 28 to 19 computations (32.1% saved)

regimes333.0ms (8.4%)

Accuracy

Total 5.5b remaining (98.7%)

Threshold costs 0b (0%)

Compiler

Compiled 4109 to 3176 computations (22.7% saved)

bsearch1.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	57
1	26	57
2	26	57

end1.0ms (0%)

Compiler: Compiled 40 to 25 computations (37.5% saved)

sample1.6s (40.2%)

Algorithm

1×

intervals

Results

442.0ms	6087×	body	128	valid
262.0ms	752×	body	2048	valid
166.0ms	8000×	pre	128	true
137.0ms	485×	body	1024	valid
126.0ms	286×	body	4096	valid
50.0ms	242×	body	512	valid
21.0ms	148×	body	256	valid

Compiler

Compiled 94 to 64 computations (31.9% saved)

Details

analyze1.1s (28.9%)

sample50.0ms (1.3%)

simplify11.0ms (0.3%)

prune16.0ms (0.4%)

localize10.0ms (0.2%)

rewrite9.0ms (0.2%)

series99.0ms (2.5%)

simplify139.0ms (3.5%)

prune177.0ms (4.5%)

localize5.0ms (0.1%)

rewrite20.0ms (0.5%)

series102.0ms (2.6%)

simplify165.0ms (4.2%)

prune58.0ms (1.5%)

localize2.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify9.0ms (0.2%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify9.0ms (0.2%)

prune2.0ms (0.1%)

regimes333.0ms (8.4%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.6s (40.2%)

Profiling