Details

analyze1.1s (24.3%)

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 28 to 20 computations (28.6% saved)

sample93.0ms (2%)

Algorithm

1×

intervals

Results

53.0ms	194×	body	128	valid
10.0ms	21×	body	2048	valid
6.0ms	256×	pre	128	true
5.0ms	11×	body	4096	valid
4.0ms	15×	body	1024	valid
3.0ms	13×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 49 to 36 computations (26.5% saved)

simplify9.0ms (0.2%)

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

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

12.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.9b	(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	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	0.0b	(/.f64 x (sqrt.f64 (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)
✓	12.9b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series103.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

32.0ms	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
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)))))
14.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 81

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

simplify99.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

716×	`associate-/l*_binary64`
593×	`fma-def_binary64`
419×	`cancel-sign-sub-inv_binary64`
284×	`fma-neg_binary64`
229×	`sub-neg_binary64`

Counts

177 → 241

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	4370
1	734	4162
2	2294	4048
3	5226	4048

prune204.0ms (4.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	235	6	241
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	235	7	242

Error

3.2b

Counts

242 → 7

Alt Table

Status	Error	Program
	54.8b	(/.f64 p (neg.f64 x))
	56.3b	(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 4) (pow.f64 x 4)) -3 (*.f64 (/.f64 (pow.f64 p 8) (pow.f64 x 8)) -35)))))
	35.0b	(sqrt.f64 (+.f64 (/.f64 1/32 (pow.f64 (/.f64 p x) 3)) (fma.f64 (/.f64 x p) -1/4 1/2)))
	50.6b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
	53.1b	(sqrt.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
▶	12.9b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
✓	12.9b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))

Compiler

Compiled 5830 to 3930 computations (32.6% saved)

localize13.0ms (0.3%)

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	(expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)))
	0.5b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
	12.9b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series76.0ms (1.7%)

Counts

1 → 24

Calls

1 calls:

76.0ms

(expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 4 p))))) 1/2)))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 4 p))))) 1/2)))

simplify52.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

600×	`fma-neg_binary64`
424×	`distribute-rgt-neg-in_binary64`
421×	`distribute-lft-neg-in_binary64`
358×	`times-frac_binary64`
321×	`distribute-neg-frac_binary64`

Counts

35 → 47

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	800
1	198	735
2	563	717
3	2588	699
4	5003	699

prune203.0ms (4.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	238	7	245

Error

3.2b

Counts

245 → 7

Alt Table

Status	Error	Program
	54.8b	(/.f64 p (neg.f64 x))
	56.3b	(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 4) (pow.f64 x 4)) -3 (*.f64 (/.f64 (pow.f64 p 8) (pow.f64 x 8)) -35)))))
▶	34.7b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 (/.f64 x p) -1/4 1/2))))
	50.6b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
	53.1b	(sqrt.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
✓	12.9b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
✓	12.9b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))

Compiler

Compiled 5978 to 4136 computations (30.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.2b	(expm1.f64 (log1p.f64 (fma.f64 (/.f64 x p) -1/4 1/2)))
✓	1.5b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 (/.f64 x p) -1/4 1/2))))
✓	1.5b	(log1p.f64 (fma.f64 (/.f64 x p) -1/4 1/2))

series43.0ms (0.9%)

Counts

3 → 60

Calls

3 calls:

25.0ms	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 (/.f64 x p) -1/4 1/2))))
11.0ms	(log1p.f64 (fma.f64 (/.f64 x p) -1/4 1/2))
6.0ms	(expm1.f64 (log1p.f64 (fma.f64 (/.f64 x p) -1/4 1/2)))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`pow1_binary64`
4×	`expm1-log1p-u_binary64`

Counts

3 → 37

Calls

3 calls:

1.0ms	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 (/.f64 x p) -1/4 1/2))))
0.0ms	(log1p.f64 (fma.f64 (/.f64 x p) -1/4 1/2))
0.0ms	(expm1.f64 (log1p.f64 (fma.f64 (/.f64 x p) -1/4 1/2)))

simplify68.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

508×	`times-frac_binary64`
298×	`associate-/l*_binary64`
254×	`associate-/r*_binary64`
245×	`fma-neg_binary64`
242×	`fma-def_binary64`

Counts

97 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	133	1622
1	329	1518
2	1104	1451
3	4755	1449
4	4947	1449

prune61.0ms (1.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	95	7	102

Error

3.2b

Counts

102 → 7

Alt Table

Status	Error	Program
	54.8b	(/.f64 p (neg.f64 x))
	56.3b	(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 4) (pow.f64 x 4)) -3 (*.f64 (/.f64 (pow.f64 p 8) (pow.f64 x 8)) -35)))))
✓	34.7b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 (/.f64 x p) -1/4 1/2))))
▶	50.6b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
	53.1b	(sqrt.f64 (/.f64 (pow.f64 p 2) (pow.f64 x 2)))
✓	12.9b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
✓	12.9b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))

Compiler

Compiled 1741 to 1202 computations (31% 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)
✓	22.7b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

series50.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

31.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
12.0ms	(/.f64 (*.f64 x x) p)
6.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

rewrite22.0ms (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))
4.0ms	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
4.0ms	(/.f64 (*.f64 x x) p)

simplify140.0ms (3%)

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 → 192

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

prune56.0ms (1.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	2	1	3
Picked	1	0	1
Done	0	3	3
Total	194	5	199

Error

Counts

199 → 5

Alt Table

Status	Error	Program
✓	34.7b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 (/.f64 x p) -1/4 1/2))))
	54.8b	(/.f64 p (neg.f64 x))
✓	12.9b	(sqrt.f64 (expm1.f64 (log1p.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	51.0b	(/.f64 p x)
✓	12.9b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))

Compiler

Compiled 2774 to 785 computations (71.7% saved)

regimes440.0ms (9.6%)

Accuracy

Total 5.8b remaining (98.7%)

Threshold costs 0b (0%)

Counts

54 → 2

Compiler

Compiled 5480 to 4259 computations (22.3% saved)

bsearch1.0ms (0%)

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

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	61
1	29	61
2	28	61

end1.0ms (0%)

Compiler: Compiled 42 to 26 computations (38.1% saved)

sample1.7s (37.1%)

Algorithm

1×

intervals

Results

447.0ms	6026×	body	128	valid
293.0ms	805×	body	2048	valid
195.0ms	8000×	pre	128	true
151.0ms	533×	body	1024	valid
112.0ms	261×	body	4096	valid
58.0ms	265×	body	512	valid
15.0ms	110×	body	256	valid

Compiler

Compiled 130 to 90 computations (30.8% saved)

Details

analyze1.1s (24.3%)

sample93.0ms (2%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series103.0ms (2.2%)

rewrite10.0ms (0.2%)

simplify99.0ms (2.2%)

prune204.0ms (4.4%)

localize13.0ms (0.3%)

series76.0ms (1.7%)

rewrite1.0ms (0%)

simplify52.0ms (1.1%)

prune203.0ms (4.4%)

localize8.0ms (0.2%)

series43.0ms (0.9%)

rewrite3.0ms (0.1%)

simplify68.0ms (1.5%)

prune61.0ms (1.3%)

localize5.0ms (0.1%)

series50.0ms (1.1%)

rewrite22.0ms (0.5%)

simplify140.0ms (3%)

prune56.0ms (1.2%)

regimes440.0ms (9.6%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.7s (37.1%)

Profiling