Details

analyze476.0ms (8.9%)

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)

sample1.4s (26%)

Results

872.0ms	8256×	body	128	valid
256.0ms	2562×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify197.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

767×	`unsub-neg_binary64`
741×	`*-commutative_binary64`
699×	`fma-def_binary64`
598×	`fma-neg_binary64`
465×	`distribute-neg-out_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	19	15
2	29	15
3	57	15
4	118	15
5	278	15
6	529	15
7	1007	15
8	1781	15
9	2585	15
10	2834	15
11	3141	15
12	3371	15
13	3485	15
14	3485	15
15	4444	15
16	4284	15
17	4604	15
18	4604	15
19	5103	15

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

24.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	24.7b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
✓	2.4b	(-.f64 (.f64 y y) (.f64 z z))
✓	24.0b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series59.0ms (1.1%)

Counts

3 → 84

Calls

3 calls:

37.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
16.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
6.0ms	(-.f64 (.f64 y y) (.f64 z z))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 62

Calls

3 calls:

8.0ms	(.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))
3.0ms	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))
3.0ms	(-.f64 (.f64 y y) (.f64 z z))

simplify99.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-def_binary64`
337×	`fma-neg_binary64`
316×	`cancel-sign-sub-inv_binary64`
268×	`neg-mul-1_binary64`
187×	`distribute-rgt-neg-in_binary64`

Counts

146 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	206	2931
1	582	2842
2	2289	2771
3	4556	2771
4	5028	2771

prune96.0ms (1.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	174	5	179
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	5	180

Error

0.2b

Counts

180 → 5

Alt Table

Status	Error	Program
▶	25.4b	(.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))))) (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))))) (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))))
	30.3b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
	36.1b	(fma.f64 y x (fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (.f64 (.f64 (/.f64 (pow.f64 z 4) (pow.f64 y 3)) x) -1/8)))
	31.1b	(*.f64 x (neg.f64 y))
	28.9b	(*.f64 x y)

Compiler

Compiled 3747 to 1669 computations (55.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))))) (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))))
	2.4b	(-.f64 (.f64 y y) (.f64 z z))
✓	3.6b	(cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z)))))
	24.0b	(sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))

series1.2s (23.1%)

Counts

2 → 72

Calls

2 calls:

628.0ms	(cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z)))))
600.0ms	(.f64 (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))))) (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`associate-*r/_binary64`
14×	`cbrt-div_binary64`
14×	`sqrt-div_binary64`
9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

2 → 54

Calls

2 calls:

6.0ms	(.f64 (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))))) (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))))
5.0ms	(cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z)))))

simplify146.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

372×	`fma-neg_binary64`
362×	`associate-r_binary64`
262×	`associate-l_binary64`
221×	`sub-neg_binary64`
206×	`*-commutative_binary64`

Counts

126 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	378	5280
1	1091	4938
2	4202	4686
3	4999	4686
4	5100	4686

prune341.0ms (6.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	584	0	584
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	584	5	589

Error

0.2b

Counts

589 → 5

Alt Table

Status	Error	Program
✓	25.4b	(.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))))) (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))))) (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))))
	30.3b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
	36.1b	(fma.f64 y x (fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (.f64 (.f64 (/.f64 (pow.f64 z 4) (pow.f64 y 3)) x) -1/8)))
	31.1b	(*.f64 x (neg.f64 y))
▶	28.9b	(*.f64 x y)

Compiler

Compiled 28449 to 8929 computations (68.6% saved)

localize2.0ms (0%)

prune4.0ms (0.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	1	1
Total	5	5

Error

0.2b

Counts

5 → 5

Alt Table

Status	Error	Program
✓	25.4b	(.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))))) (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))))) (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))))
▶	30.3b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
	36.1b	(fma.f64 y x (fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (.f64 (.f64 (/.f64 (pow.f64 z 4) (pow.f64 y 3)) x) -1/8)))
	31.1b	(*.f64 x (neg.f64 y))
✓	28.9b	(*.f64 x y)

Compiler

Compiled 138 to 77 computations (44.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
✓	0.0b	(sqrt.f64 (+.f64 y z))
✓	0.3b	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))

series76.0ms (1.4%)

Counts

3 → 60

Calls

3 calls:

37.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
21.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))
18.0ms	(sqrt.f64 (+.f64 y z))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-div_binary64`
24×	`add-sqr-sqrt_binary64`
17×	`sqrt-prod_binary64`
15×	`*-un-lft-identity_binary64`
13×	`pow1_binary64`

Counts

3 → 91

Calls

3 calls:

9.0ms	(*.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))
8.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
2.0ms	(sqrt.f64 (+.f64 y z))

simplify126.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-def_binary64`
339×	`cancel-sign-sub-inv_binary64`
280×	`fma-neg_binary64`
259×	`distribute-rgt-in_binary64`
225×	`distribute-lft-in_binary64`

Counts

151 → 216

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	264	3378
1	720	3270
2	2340	3086
3	4838	3085
4	4945	3085
5	4993	3085

prune175.0ms (3.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	215	6	221

Error

0.1b

Counts

221 → 6

Alt Table

Status	Error	Program
✓	25.4b	(.f64 (.f64 (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z))))) (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (.f64 z z)))))) (cbrt.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 y y) (*.f64 z z))))))
✓	30.3b	(.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))
	36.1b	(fma.f64 y x (fma.f64 (.f64 (/.f64 (.f64 z z) y) x) -1/2 (.f64 (.f64 (/.f64 (pow.f64 z 4) (pow.f64 y 3)) x) -1/8)))
	31.1b	(*.f64 x (neg.f64 y))
✓	28.9b	(*.f64 x y)
	30.7b	(.f64 (.f64 (cbrt.f64 (.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))) (cbrt.f64 (.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z)))))) (cbrt.f64 (.f64 x (.f64 (sqrt.f64 (+.f64 y z)) (sqrt.f64 (-.f64 y z))))))

Compiler

Compiled 4823 to 1964 computations (59.3% saved)

regimes686.0ms (12.9%)

Accuracy

Total 0.5b remaining (81.2%)

Threshold costs 0.5b (81.2%)

Counts

28 → 2

Compiler

Compiled 6922 to 3461 computations (50% saved)

bsearch62.0ms (1.2%)

Steps

Iters	Range		Point
2	-1.189575496443039e-259	3.4606458152099164e-212	-4.930641161483513e-296

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (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

end77.0ms (1.4%)

Compiler: Compiled 160 to 76 computations (52.5% saved)

Details

analyze476.0ms (8.9%)

sample1.4s (26%)

simplify197.0ms (3.7%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series59.0ms (1.1%)

rewrite16.0ms (0.3%)

simplify99.0ms (1.9%)

prune96.0ms (1.8%)

localize10.0ms (0.2%)

series1.2s (23.1%)

rewrite19.0ms (0.3%)

simplify146.0ms (2.7%)

prune341.0ms (6.4%)

localize2.0ms (0%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series76.0ms (1.4%)

rewrite27.0ms (0.5%)

simplify126.0ms (2.4%)

prune175.0ms (3.3%)

regimes686.0ms (12.9%)

bsearch62.0ms (1.2%)

simplify3.0ms (0.1%)

end77.0ms (1.4%)

Profiling