Details

analyze1.1s (19.8%)

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)

sample83.0ms (1.5%)

Algorithm

1×

intervals

Results

19.0ms	197×	body	128	valid
8.0ms	24×	body	2048	valid
6.0ms	256×	pre	128	true
4.0ms	15×	body	1024	valid
4.0ms	9×	body	4096	valid
2.0ms	8×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 49 to 36 computations (26.5% saved)

simplify10.0ms (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

prune4.0ms (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

12.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	12.6b	(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)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 p (.f64 4 p)))
✓	0.0b	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
✓	0.4b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
✓	13.0b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series93.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

39.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
29.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
13.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))
11.0ms	(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 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
0.0ms	(fma.f64 x x (.f64 p (.f64 4 p)))

simplify121.0ms (2.2%)

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 → 214

Iterations

Useful iterations: 2 (0.0ms)

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

prune205.0ms (3.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	209	5	214
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	210	5	215

Error

5.8b

Counts

215 → 5

Alt Table

Status	Error	Program
▶	12.6b	(sqrt.f64 (exp.f64 (log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	52.3b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))
	58.3b	(sqrt.f64 (-.f64 (+.f64 (.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (*.f64 35 (/.f64 (pow.f64 p 8) (pow.f64 x 8))))))
	12.7b	(sqrt.f64 (fma.f64 1/2 (log.f64 (exp.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))))) 1/2))
	12.7b	(sqrt.f64 (log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))

Compiler

Compiled 5105 to 3418 computations (33% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)))
	0.4b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
✓	0.5b	(log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	13.0b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series75.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

45.0ms	(log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
29.0ms	(exp.f64 (log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms	(exp.f64 (log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)))
1.0ms	(log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))

simplify112.0ms (2%)

Algorithm

1×	egg-herbie

Rules

513×	`times-frac_binary64`
306×	`sub-neg_binary64`
306×	`fma-def_binary64`
240×	`associate-r_binary64`
227×	`associate-/r*_binary64`

Counts

79 → 108

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	145	2078
1	378	1898
2	1049	1841
3	4470	1774
4	4855	1763
5	4969	1763

prune197.0ms (3.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	205	2	207
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	208	4	212

Error

5.7b

Counts

212 → 4

Alt Table

Status	Error	Program
	58.3b	(sqrt.f64 (-.f64 (+.f64 (.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (*.f64 35 (/.f64 (pow.f64 p 8) (pow.f64 x 8))))))
	12.7b	(sqrt.f64 (fma.f64 1/2 (log.f64 (exp.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))))) 1/2))
	52.7b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 p x) 4) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 10 (pow.f64 (/.f64 x p) 6)))))
▶	12.6b	(sqrt.f64 (pow.f64 (E.f64) (log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))

Compiler

Compiled 5018 to 3533 computations (29.6% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (E.f64) (log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)))
	0.4b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
	0.5b	(log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	13.0b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series64.0ms (1.1%)

Counts

1 → 24

Calls

1 calls:

64.0ms

(pow.f64 (E.f64) (log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 4 p))))) 1/2)))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow-unpow_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`pow1_binary64`

Counts

1 → 24

Calls

1 calls:

6.0ms

(pow.f64 (E.f64) (log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (*.f64 p (*.f64 4 p))))) 1/2)))

simplify90.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-neg_binary64`
593×	`times-frac_binary64`
277×	`associate-r_binary64`
257×	`associate-/l*_binary64`
218×	`associate-/r*_binary64`

Counts

48 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	1505
1	298	1350
2	828	1318
3	3988	1307
4	4985	1307
5	4953	1307

prune239.0ms (4.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	218	4	222

Error

5.7b

Counts

222 → 4

Alt Table

Status	Error	Program
	58.3b	(sqrt.f64 (-.f64 (+.f64 (.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (*.f64 35 (/.f64 (pow.f64 p 8) (pow.f64 x 8))))))
▶	12.7b	(sqrt.f64 (fma.f64 1/2 (log.f64 (exp.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))))) 1/2))
	52.7b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 p x) 4) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 10 (pow.f64 (/.f64 x p) 6)))))
✓	12.6b	(sqrt.f64 (pow.f64 (E.f64) (log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))

Compiler

Compiled 5749 to 3949 computations (31.3% saved)

localize12.0ms (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)))))
✓	0.4b	(fma.f64 1/2 (log.f64 (exp.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))))) 1/2)
✓	3.4b	(log.f64 (exp.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))))
	13.0b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))

series54.0ms (1%)

Counts

2 → 48

Calls

2 calls:

27.0ms	(log.f64 (exp.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))))
27.0ms	(fma.f64 1/2 (log.f64 (exp.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))))) 1/2)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`log-pow_binary64`
22×	`exp-prod_binary64`
18×	`times-frac_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

2 → 46

Calls

2 calls:

5.0ms	(log.f64 (exp.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))))
0.0ms	(fma.f64 1/2 (log.f64 (exp.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))))) 1/2)

simplify87.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

471×	`times-frac_binary64`
264×	`fma-def_binary64`
261×	`sub-neg_binary64`
236×	`unswap-sqr_binary64`
227×	`associate-r_binary64`

Counts

94 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	184	2147
1	416	2010
2	1105	1976
3	4291	1931
4	4944	1931

prune277.0ms (4.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	277	4	281

Error

5.7b

Counts

281 → 4

Alt Table

Status	Error	Program
	58.3b	(sqrt.f64 (-.f64 (+.f64 (.f64 10 (/.f64 (pow.f64 p 6) (pow.f64 x 6))) (/.f64 (pow.f64 p 2) (pow.f64 x 2))) (+.f64 (.f64 3 (/.f64 (pow.f64 p 4) (pow.f64 x 4))) (*.f64 35 (/.f64 (pow.f64 p 8) (pow.f64 x 8))))))
✓	12.7b	(sqrt.f64 (fma.f64 1/2 (log.f64 (exp.f64 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))))) 1/2))
	52.7b	(sqrt.f64 (fma.f64 (pow.f64 (/.f64 p x) 4) -3 (fma.f64 (/.f64 p x) (/.f64 p x) (/.f64 10 (pow.f64 (/.f64 x p) 6)))))
✓	12.6b	(sqrt.f64 (pow.f64 (E.f64) (log.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))

Compiler

Compiled 7214 to 4959 computations (31.3% saved)

regimes1.1s (19.1%)

Accuracy

Total 0.0b remaining (0.2%)

Threshold costs 0.0b (0.2%)

Counts

140 → 2

Compiler

Compiled 15329 to 12040 computations (21.5% saved)

bsearch4.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`e-exp-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	83
1	39	83
2	41	83
3	40	83

end1.0ms (0%)

Compiler: Compiled 57 to 37 computations (35.1% saved)

sample1.6s (29.1%)

Algorithm

1×

intervals

Results

445.0ms	6144×	body	128	valid
269.0ms	778×	body	2048	valid
176.0ms	8000×	pre	128	true
126.0ms	443×	body	1024	valid
120.0ms	281×	body	4096	valid
48.0ms	228×	body	512	valid
21.0ms	126×	body	256	valid

Compiler

Compiled 190 to 134 computations (29.5% saved)

Details

analyze1.1s (19.8%)

sample83.0ms (1.5%)

simplify10.0ms (0.2%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series93.0ms (1.6%)

rewrite9.0ms (0.2%)

simplify121.0ms (2.2%)

prune205.0ms (3.6%)

localize15.0ms (0.3%)

series75.0ms (1.3%)

rewrite4.0ms (0.1%)

simplify112.0ms (2%)

prune197.0ms (3.5%)

localize14.0ms (0.3%)

series64.0ms (1.1%)

rewrite8.0ms (0.1%)

simplify90.0ms (1.6%)

prune239.0ms (4.2%)

localize12.0ms (0.2%)

series54.0ms (1%)

rewrite9.0ms (0.2%)

simplify87.0ms (1.5%)

prune277.0ms (4.9%)

regimes1.1s (19.1%)

bsearch4.0ms (0.1%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.6s (29.1%)

Profiling