Details

analyze1.2s (18.9%)

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 28 to 20 computations (28.6% saved)

sample63.0ms (1%)

Algorithm

1×

intervals

Results

14.0ms	206×	body	128	valid
6.0ms	19×	body	2048	valid
5.0ms	256×	pre	128	true
4.0ms	11×	body	1024	valid
3.0ms	8×	body	4096	valid
1.0ms	5×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 49 to 36 computations (26.5% saved)

simplify7.0ms (0.1%)

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

11.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	11.2b	(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)

localize9.0ms (0.1%)

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)))))
✓	1.7b	(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))))

series179.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

62.0ms	(/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p)))))
57.0ms	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))
32.0ms	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
28.0ms	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)

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)

simplify101.0ms (1.6%)

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

prune229.0ms (3.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	237	4	241
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	237	5	242

Error

1.9b

Counts

242 → 5

Alt Table

Status	Error	Program
	11.7b	(.f64 (sqrt.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))) (sqrt.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 4 p))))) 1/2))))
	55.1b	(-.f64 (*.f64 3/2 (pow.f64 (/.f64 p x) 3)) (/.f64 p x))
✓	11.2b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
▶	11.2b	(log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	52.8b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

Compiler

Compiled 5786 to 3894 computations (32.7% saved)

localize13.0ms (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)))))
✓	1.2b	(log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))
	1.7b	(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))))

series35.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

34.0ms

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

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`log-pow_binary64`
6×	`exp-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`

Counts

1 → 20

Calls

1 calls:

2.0ms

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

simplify90.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

816×	`times-frac_binary64`
697×	`fma-neg_binary64`
385×	`associate-/l*_binary64`
330×	`associate-/r*_binary64`
233×	`associate-r_binary64`

Counts

44 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1298
1	297	1206
2	938	1153
3	4720	1151
4	5303	1151

prune321.0ms (5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	250	2	252
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	252	5	257

Error

1.9b

Counts

257 → 5

Alt Table

Status	Error	Program
▶	11.2b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))))
	55.1b	(-.f64 (*.f64 3/2 (pow.f64 (/.f64 p x) 3)) (/.f64 p x))
✓	11.2b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
	11.7b	(.f64 (sqrt.f64 (log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))) (sqrt.f64 (log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 4 p))))) 1/2))))))
	52.8b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

Compiler

Compiled 6617 to 4624 computations (30.1% saved)

localize15.0ms (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)))))
✓	1.2b	(log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)))))
	1.7b	(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))))

series93.0ms (1.5%)

Counts

1 → 24

Calls

1 calls:

93.0ms

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

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`log-pow_binary64`
7×	`sqrt-pow1_binary64`
6×	`log-prod_binary64`
6×	`sqrt-prod_binary64`
6×	`exp-prod_binary64`

Counts

1 → 25

Calls

1 calls:

3.0ms

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

simplify96.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/r*_binary64`
555×	`associate-/l*_binary64`
474×	`fma-def_binary64`
317×	`fma-neg_binary64`
249×	`associate-*l/_binary64`

Counts

49 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	2209
1	442	1819
2	1464	1680
3	4523	1656
4	4890	1656
5	4922	1656

prune690.0ms (10.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	517	1	518
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	518	5	523

Error

1.8b

Counts

523 → 5

Alt Table

Status	Error	Program
	55.1b	(-.f64 (*.f64 3/2 (pow.f64 (/.f64 p x) 3)) (/.f64 p x))
✓	11.2b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
▶	11.1b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2))))))))
	11.7b	(.f64 (sqrt.f64 (log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))) (sqrt.f64 (log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 4 p))))) 1/2))))))
	52.8b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

Compiler

Compiled 24351 to 17608 computations (27.7% saved)

localize31.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.7b	(fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2)
✓	1.7b	(log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2)))
	16.6b	(sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))
✓	16.6b	(sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))

series42.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2)))
12.0ms	(sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
4×	`log-prod_binary64`
4×	`log-pow_binary64`

Counts

2 → 33

Calls

2 calls:

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

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

522×	`times-frac_binary64`
275×	`unswap-sqr_binary64`
268×	`associate-/l*_binary64`
261×	`sub-neg_binary64`
249×	`fma-def_binary64`

Counts

81 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	149	1778
1	359	1674
2	1008	1640
3	4421	1622
4	5124	1622

prune265.0ms (4.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	203	5	208

Error

1.8b

Counts

208 → 5

Alt Table

Status	Error	Program
	55.1b	(-.f64 (*.f64 3/2 (pow.f64 (/.f64 p x) 3)) (/.f64 p x))
✓	11.2b	(sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))
✓	11.1b	(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (log.f64 (exp.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 p (.f64 p 4) (.f64 x x)))) 1/2))))))))
	11.7b	(.f64 (sqrt.f64 (log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (.f64 4 p))))) 1/2))))) (sqrt.f64 (log.f64 (exp.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 x (sqrt.f64 (fma.f64 x x (.f64 p (*.f64 4 p))))) 1/2))))))
	52.8b	(sqrt.f64 (/.f64 p (/.f64 (*.f64 x x) p)))

Compiler

Compiled 9288 to 6699 computations (27.9% saved)

regimes1.1s (17.4%)

Accuracy

Total 3.0b remaining (50.1%)

Threshold costs 0b (0%)

Counts

153 → 2

Compiler

Compiled 22430 to 16726 computations (25.4% saved)

bsearch6.0ms (0.1%)

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

simplify3.0ms (0%)

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)

sample1.7s (26.1%)

Algorithm

1×

intervals

Results

439.0ms	6051×	body	128	valid
275.0ms	806×	body	2048	valid
176.0ms	8000×	pre	128	true
136.0ms	481×	body	1024	valid
122.0ms	280×	body	4096	valid
53.0ms	254×	body	512	valid
20.0ms	128×	body	256	valid

Compiler

Compiled 190 to 133 computations (30% saved)

Details

analyze1.2s (18.9%)

sample63.0ms (1%)

simplify7.0ms (0.1%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series179.0ms (2.8%)

rewrite10.0ms (0.2%)

simplify101.0ms (1.6%)

prune229.0ms (3.6%)

localize13.0ms (0.2%)

series35.0ms (0.5%)

rewrite3.0ms (0.1%)

simplify90.0ms (1.4%)

prune321.0ms (5%)

localize15.0ms (0.2%)

series93.0ms (1.5%)

rewrite6.0ms (0.1%)

simplify96.0ms (1.5%)

prune690.0ms (10.8%)

localize31.0ms (0.5%)

series42.0ms (0.7%)

rewrite4.0ms (0.1%)

simplify79.0ms (1.2%)

prune265.0ms (4.2%)

regimes1.1s (17.4%)

bsearch6.0ms (0.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.7s (26.1%)

Profiling