Details

analyze652.0ms (14.2%)

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
0%	99.9%	0.1%	6
0%	81.1%	18.9%	7
6.2%	74.9%	18.9%	8
9.4%	65.5%	25.1%	9
15.6%	48.4%	36%	10
20.3%	43.1%	36.6%	11
22.6%	36%	41.4%	12
27.1%	25.1%	47.8%	13
29.5%	22.5%	48%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample28.0ms (0.6%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
2.0ms	52×	body	128	nan
1.0ms	19×	body	128	invalid

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify331.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

3990×	`distribute-rgt-in_binary64`
2232×	`associate--r-_binary64`
1285×	`sub-neg_binary64`
783×	`unsub-neg_binary64`
741×	`*-commutative_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	18	15
2	28	15
3	53	15
4	103	15
5	229	15
6	354	15
7	732	15
8	1115	15
9	1919	15
10	2168	15
11	2475	15
12	2705	15
13	2819	15
14	2819	15
15	3778	15
16	3618	15
17	3938	15
18	3938	15
19	3858	15
20	4018	15
21	4098	15
22	4098	15
23	4098	15
24	4863	15
25	4880	15
26	10529	15

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

26.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	26.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 26 to 16 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

4.2b	(-.f64 (.f64 y y) (.f64 z z))
25.8b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

13.4b

Rules

4×	`sqrt-prod_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 29

Calls

2 calls:

3.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
3.0ms	(-.f64 (.f64 y y) (.f64 z z))

Compiler

Compiled 520 to 131 computations (74.8% saved)

series36.0ms (0.8%)

Error

0.1b

Counts

2 → 21

Calls

2 calls:

17.0ms	(-.f64 (.f64 y y) (.f64 z z))
13.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

Compiler

Compiled 521 to 394 computations (24.4% saved)

simplify54.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

769×	`unswap-sqr_binary64`
468×	`times-frac_binary64`
328×	`*-commutative_binary64`
203×	`unsub-neg_binary64`
153×	`associate-l_binary64`

Counts

50 → 32

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	67	674
1	147	596
2	356	596
3	1202	596
4	2471	596
5	4957	596

prune15.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Error

0.1b

Counts

33 → 4

Alt Table

Status	Error	Program
▶	30.8b	(.f64 x (.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z))))
✓	26.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
	31.7b	(*.f64 x (neg.f64 y))
	32.2b	(.f64 x (-.f64 y (.f64 1/2 (/.f64 (*.f64 z z) y))))

Compiler

Compiled 352 to 171 computations (51.4% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (-.f64 y z))
0.3b	(*.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z)))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

22×	`add-sqr-sqrt_binary64`
18×	`sqrt-prod_binary64`
14×	`sqrt-div_binary64`
13×	`*-un-lft-identity_binary64`
8×	`associate-r_binary64`

Counts

2 → 59

Calls

2 calls:

9.0ms	(*.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z)))
3.0ms	(sqrt.f64 (-.f64 y z))

Compiler

Compiled 966 to 257 computations (73.4% saved)

series30.0ms (0.6%)

Error

0.1b

Counts

2 → 17

Calls

2 calls:

13.0ms	(*.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z)))
12.0ms	(sqrt.f64 (-.f64 y z))

Compiler

Compiled 645 to 459 computations (28.8% saved)

simplify109.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

923×	`times-frac_binary64`
537×	`distribute-rgt-in_binary64`
497×	`distribute-lft-in_binary64`
405×	`cancel-sign-sub-inv_binary64`
350×	`*-commutative_binary64`

Counts

76 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	128	1242
1	267	1221
2	649	1175
3	1603	1172
4	3613	1172
5	4228	1172
6	5138	1172

prune27.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	51	3	54
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	51	7	58

Error

0.1b

Counts

58 → 7

Alt Table

Status	Error	Program
	31.0b	(.f64 x (.f64 (*.f64 (sqrt.f64 (+.f64 y z)) (fabs.f64 (cbrt.f64 (-.f64 y z)))) (sqrt.f64 (cbrt.f64 (-.f64 y z)))))
▶	30.9b	(.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z))))))
	39.0b	(.f64 x (/.f64 (.f64 (+.f64 y z) (sqrt.f64 (-.f64 y z))) (sqrt.f64 (+.f64 y z))))
✓	30.8b	(.f64 x (.f64 (sqrt.f64 (+.f64 z y)) (sqrt.f64 (-.f64 y z))))
✓	26.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
	31.7b	(*.f64 x (neg.f64 y))
	32.2b	(.f64 x (-.f64 y (.f64 1/2 (/.f64 (*.f64 z z) y))))

Compiler

Compiled 996 to 397 computations (60.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 y z)))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 z y)))
0.1b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z)))))
0.2b	(*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z))))

rewrite107.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

116×	`sqrt-div_binary64`
65×	`sqrt-prod_binary64`
50×	`add-sqr-sqrt_binary64`
32×	`frac-times_binary64`
26×	`*-un-lft-identity_binary64`

Counts

4 → 150

Calls

4 calls:

17.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z)))))
12.0ms	(*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z))))
6.0ms	(sqrt.f64 (sqrt.f64 (+.f64 y z)))
3.0ms	(sqrt.f64 (sqrt.f64 (+.f64 z y)))

Compiler

Compiled 3744 to 820 computations (78.1% saved)

series108.0ms (2.4%)

Error

0.1b

Counts

4 → 41

Calls

4 calls:

27.0ms	(*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z))))
25.0ms	(sqrt.f64 (sqrt.f64 (+.f64 z y)))
25.0ms	(sqrt.f64 (sqrt.f64 (+.f64 y z)))
15.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z)))))

Compiler

Compiled 2368 to 1721 computations (27.3% saved)

simplify262.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

421×	`*-commutative_binary64`
378×	`distribute-rgt-in_binary64`
340×	`distribute-lft-in_binary64`
247×	`cancel-sign-sub-inv_binary64`
217×	`associate-r_binary64`

Counts

191 → 148

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	270	4854
1	574	4465
2	1329	4288
3	2242	4288
4	4766	4227
5	4978	4227
6	4995	4227
7	4999	4227
8	4945	4227

prune59.0ms (1.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	0	4	4
Picked	0	1	1
Done	1	1	2
Total	148	7	155

Error

0.1b

Counts

155 → 7

Alt Table

Status	Error	Program
	32.2b	(.f64 x (-.f64 y (.f64 1/2 (/.f64 (*.f64 z z) y))))
▶	31.0b	(.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (.f64 (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 y z)))))))
	31.0b	(.f64 x (.f64 (*.f64 (sqrt.f64 (+.f64 y z)) (fabs.f64 (cbrt.f64 (-.f64 y z)))) (sqrt.f64 (cbrt.f64 (-.f64 y z)))))
✓	30.9b	(.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z))))))
	39.0b	(.f64 x (/.f64 (.f64 (+.f64 y z) (sqrt.f64 (-.f64 y z))) (sqrt.f64 (+.f64 y z))))
✓	26.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
	31.7b	(*.f64 x (neg.f64 y))

Compiler

Compiled 3129 to 1003 computations (67.9% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 z y)))
0.1b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (.f64 (*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 y z))))))
0.2b	(*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y)))))
0.2b	(.f64 (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 y z)))))

rewrite228.0ms (5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

640×	`sqrt-div_binary64`
168×	`frac-times_binary64`
152×	`sqrt-prod_binary64`
144×	`add-sqr-sqrt_binary64`
107×	`rem-sqrt-square_binary64`

Counts

4 → 271

Calls

4 calls:

29.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (.f64 (*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 y z))))))
27.0ms	(.f64 (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 y z)))))
16.0ms	(*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y)))))
3.0ms	(sqrt.f64 (sqrt.f64 (+.f64 z y)))

Compiler

Compiled 10536 to 2143 computations (79.7% saved)

series118.0ms (2.6%)

Error

0.1b

Counts

4 → 38

Calls

4 calls:

30.0ms	(.f64 (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 y z)))))
30.0ms	(*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y)))))
29.0ms	(sqrt.f64 (sqrt.f64 (+.f64 z y)))
13.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (.f64 (*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 y z))))))

Compiler

Compiled 2566 to 1841 computations (28.3% saved)

simplify396.0ms (8.6%)

Algorithm

1×	egg-herbie

Rules

772×	`associate-r_binary64`
514×	`*-commutative_binary64`
308×	`cancel-sign-sub-inv_binary64`
233×	`unswap-sqr_binary64`
191×	`sub-neg_binary64`

Counts

309 → 245

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	478	12886
1	1183	12454
2	2480	12134
3	3762	11921
4	4808	11921
5	4877	11921

prune97.0ms (2.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	245	7	252

Error

0.1b

Counts

252 → 7

Alt Table

Status	Error	Program
	32.2b	(.f64 x (-.f64 y (.f64 1/2 (/.f64 (*.f64 z z) y))))
	31.0b	(.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (.f64 (.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))))) (sqrt.f64 (sqrt.f64 (sqrt.f64 (+.f64 y z)))))))
	31.0b	(.f64 x (.f64 (*.f64 (sqrt.f64 (+.f64 y z)) (fabs.f64 (cbrt.f64 (-.f64 y z)))) (sqrt.f64 (cbrt.f64 (-.f64 y z)))))
	30.9b	(.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 z y))) (*.f64 (sqrt.f64 (-.f64 y z)) (sqrt.f64 (sqrt.f64 (+.f64 y z))))))
	39.0b	(.f64 x (/.f64 (.f64 (+.f64 y z) (sqrt.f64 (-.f64 y z))) (sqrt.f64 (+.f64 y z))))
	26.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
	31.7b	(*.f64 x (neg.f64 y))

Compiler

Compiled 7836 to 2058 computations (73.7% saved)

regimes659.0ms (14.4%)

Accuracy

Total 0.6b remaining (79.9%)

Threshold costs 0.6b (79.9%)

Compiler

Compiled 5156 to 2932 computations (43.1% saved)

bsearch236.0ms (5.1%)

Steps

Iters	Range		Point
11	-5.888222501381576e-239	-9.751745605867638e-268	-9.977773621263348e-268

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	17	16
2	24	16
3	29	16
4	32	16
5	33	16
6	33	16

end0.0ms (0%)

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

sample921.0ms (20.1%)

Algorithm

1×

intervals

Results

363.0ms	8000×	body	128	valid
82.0ms	1860×	body	128	nan
37.0ms	689×	body	128	invalid

Compiler

Compiled 154 to 96 computations (37.7% saved)

Details

analyze652.0ms (14.2%)

sample28.0ms (0.6%)

simplify331.0ms (7.2%)

prune1.0ms (0%)

localize6.0ms (0.1%)

rewrite22.0ms (0.5%)

series36.0ms (0.8%)

simplify54.0ms (1.2%)

prune15.0ms (0.3%)

localize7.0ms (0.2%)

rewrite35.0ms (0.8%)

series30.0ms (0.6%)

simplify109.0ms (2.4%)

prune27.0ms (0.6%)

localize12.0ms (0.3%)

rewrite107.0ms (2.3%)

series108.0ms (2.4%)

simplify262.0ms (5.7%)

prune59.0ms (1.3%)

localize20.0ms (0.4%)

rewrite228.0ms (5%)

series118.0ms (2.6%)

simplify396.0ms (8.6%)

prune97.0ms (2.1%)

regimes659.0ms (14.4%)

bsearch236.0ms (5.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample921.0ms (20.1%)

Profiling