Details

analyze153.0ms (4.5%)

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
12.5%	87.4%	0.1%	5
31.2%	68.7%	0.1%	6
46.8%	53.1%	0.1%	7
60.9%	39%	0.1%	8
67.9%	31.2%	0.9%	9
74.5%	22.2%	3.2%	10
77.9%	17.2%	5%	11
81.1%	11.8%	7.1%	12
82.7%	9%	8.3%	13
84.3%	6.1%	9.7%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample119.0ms (3.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify88.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1151×	`distribute-rgt-in_binary64`
1143×	`distribute-lft-in_binary64`
971×	`fma-def_binary64`
653×	`associate-/l*_binary64`
535×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	22	14
2	30	14
3	75	14
4	112	14
5	222	14
6	406	14
7	419	14
8	783	14
9	937	14
10	1259	14
11	1611	14
12	1778	14
13	2015	14
14	2939	14
15	3245	14
16	5075	14

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

8.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	8.9b	(/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))
▶	8.9b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

Compiler

Compiled 73 to 45 computations (38.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (/.f64 x y) x)
✓	8.3b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

series23.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

16.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
7.0ms	(fma.f64 x (/.f64 x y) x)

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
4×	`associate-/r*_binary64`

Counts

2 → 45

Calls

2 calls:

4.0ms	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
0.0ms	(fma.f64 x (/.f64 x y) x)

simplify108.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

1032×	`fma-neg_binary64`
526×	`cancel-sign-sub-inv_binary64`
338×	`sub-neg_binary64`
265×	`distribute-rgt-in_binary64`
240×	`associate-/l/_binary64`

Counts

93 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1641
1	245	1554
2	714	1484
3	2409	1453
4	4439	1453
5	5061	1453

prune93.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	69	7	76

Error

0.0b

Counts

76 → 7

Alt Table

Status	Error	Program
✓	8.9b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
	38.6b	(/.f64 (sqrt.f64 (fma.f64 x (/.f64 x y) x)) (/.f64 (+.f64 x 1) (sqrt.f64 (fma.f64 x (/.f64 x y) x))))
	10.0b	(/.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) (cbrt.f64 (fma.f64 x (/.f64 x y) x))) (/.f64 (+.f64 x 1) (cbrt.f64 (fma.f64 x (/.f64 x y) x))))
	33.9b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1)) 3))
	42.1b	(/.f64 (*.f64 x x) (fma.f64 x y y))
	35.4b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))
▶	8.9b	(/.f64 (+.f64 (*.f64 x (/.f64 x y)) x) (+.f64 x 1))

Compiler

Compiled 1467 to 649 computations (55.8% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 x (/.f64 x y)) x)
✓	0.1b	(*.f64 x (/.f64 x y))
✓	8.3b	(/.f64 (+.f64 (*.f64 x (/.f64 x y)) x) (+.f64 x 1))

series33.0ms (1%)

Counts

3 → 72

Calls

3 calls:

14.0ms	(/.f64 (+.f64 (*.f64 x (/.f64 x y)) x) (+.f64 x 1))
10.0ms	(*.f64 x (/.f64 x y))
9.0ms	(+.f64 (*.f64 x (/.f64 x y)) x)

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
22×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

3 → 85

Calls

3 calls:

7.0ms	(/.f64 (+.f64 (*.f64 x (/.f64 x y)) x) (+.f64 x 1))
5.0ms	(*.f64 x (/.f64 x y))
4.0ms	(+.f64 (*.f64 x (/.f64 x y)) x)

simplify114.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

614×	`fma-neg_binary64`
520×	`fma-def_binary64`
406×	`sub-neg_binary64`
360×	`associate-/l*_binary64`
317×	`times-frac_binary64`

Counts

157 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	174	2274
1	434	2154
2	1421	2082
3	4190	2074
4	5113	2074

prune84.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	153	8	161

Error

Counts

161 → 8

Alt Table

Status	Error	Program
✓	8.9b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
	38.6b	(/.f64 (sqrt.f64 (fma.f64 x (/.f64 x y) x)) (/.f64 (+.f64 x 1) (sqrt.f64 (fma.f64 x (/.f64 x y) x))))
	10.0b	(/.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) (cbrt.f64 (fma.f64 x (/.f64 x y) x))) (/.f64 (+.f64 x 1) (cbrt.f64 (fma.f64 x (/.f64 x y) x))))
	33.9b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1)) 3))
	9.2b	(/.f64 (+.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 x (cbrt.f64 y))) x) (+.f64 x 1))
▶	9.2b	(/.f64 (+.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 x y))) x) (+.f64 x 1))
	42.1b	(/.f64 (*.f64 x x) (fma.f64 x y y))
	35.4b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))

Compiler

Compiled 3140 to 1271 computations (59.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 x) (/.f64 x y))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	8.3b	(/.f64 (+.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 x y))) x) (+.f64 x 1))

series516.0ms (15.1%)

Counts

4 → 72

Calls

4 calls:

431.0ms	(*.f64 (cbrt.f64 x) (/.f64 x y))
36.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
33.0ms	(cbrt.f64 x)
16.0ms	(/.f64 (+.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 x y))) x) (+.f64 x 1))

rewrite39.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
27×	`times-frac_binary64`
24×	`cbrt-prod_binary64`

Counts

4 → 136

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 x y))) x) (+.f64 x 1))
7.0ms	(*.f64 (cbrt.f64 x) (/.f64 x y))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify131.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

841×	`fma-neg_binary64`
797×	`fma-def_binary64`
668×	`cancel-sign-sub-inv_binary64`
298×	`unswap-sqr_binary64`
206×	`associate-l_binary64`

Counts

208 → 231

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	231	3157
1	553	2718
2	2176	2597
3	3730	2515
4	4881	2515
5	5034	2515

prune157.0ms (4.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	267	0	267
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	267	8	275

Error

Counts

275 → 8

Alt Table

Status	Error	Program
✓	8.9b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))
	38.6b	(/.f64 (sqrt.f64 (fma.f64 x (/.f64 x y) x)) (/.f64 (+.f64 x 1) (sqrt.f64 (fma.f64 x (/.f64 x y) x))))
	10.0b	(/.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) (cbrt.f64 (fma.f64 x (/.f64 x y) x))) (/.f64 (+.f64 x 1) (cbrt.f64 (fma.f64 x (/.f64 x y) x))))
	33.9b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1)) 3))
▶	9.2b	(/.f64 (+.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 x (cbrt.f64 y))) x) (+.f64 x 1))
✓	9.2b	(/.f64 (+.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 x y))) x) (+.f64 x 1))
	42.1b	(/.f64 (*.f64 x x) (fma.f64 x y y))
	35.4b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))

Compiler

Compiled 6560 to 2348 computations (64.2% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(cbrt.f64 y)
✓	8.3b	(/.f64 (+.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 x (cbrt.f64 y))) x) (+.f64 x 1))

series559.0ms (16.4%)

Counts

4 → 72

Calls

4 calls:

452.0ms	(/.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
40.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
34.0ms	(/.f64 (+.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 x (cbrt.f64 y))) x) (+.f64 x 1))
33.0ms	(cbrt.f64 y)

rewrite28.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`
19×	`cbrt-prod_binary64`
15×	`times-frac_binary64`

Counts

4 → 115

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 x (cbrt.f64 y))) x) (+.f64 x 1))
4.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
4.0ms	(/.f64 x (*.f64 (cbrt.f64 y) (cbrt.f64 y)))
1.0ms	(cbrt.f64 y)

simplify123.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

453×	`associate-/l*_binary64`
419×	`unswap-sqr_binary64`
373×	`associate-*l/_binary64`
352×	`fma-def_binary64`
299×	`associate-*r/_binary64`

Counts

187 → 194

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	200	3434
1	457	2557
2	1527	2340
3	4065	2325
4	4867	2325
5	4920	2325

prune134.0ms (3.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	230	8	238

Error

Counts

238 → 8

Alt Table

Status	Error	Program
✓	9.2b	(/.f64 (+.f64 (.f64 (/.f64 x (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 x (cbrt.f64 y))) x) (+.f64 x 1))
	9.3b	(/.f64 (+.f64 (*.f64 (/.f64 (/.f64 x (cbrt.f64 y)) (cbrt.f64 y)) (/.f64 x (cbrt.f64 y))) x) (+.f64 x 1))
	10.0b	(/.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 x y) x)) (cbrt.f64 (fma.f64 x (/.f64 x y) x))) (/.f64 (+.f64 x 1) (cbrt.f64 (fma.f64 x (/.f64 x y) x))))
	33.9b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1)) 3))
✓	9.2b	(/.f64 (+.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (/.f64 x y))) x) (+.f64 x 1))
	42.1b	(/.f64 (*.f64 x x) (fma.f64 x y y))
	35.4b	(-.f64 (+.f64 1 (/.f64 x y)) (/.f64 1 y))
✓	8.9b	(/.f64 (fma.f64 x (/.f64 x y) x) (+.f64 x 1))

Compiler

Compiled 5525 to 2060 computations (62.7% saved)

regimes148.0ms (4.3%)

Accuracy

Total 0.1b remaining (84.5%)

Threshold costs 0.1b (84.5%)

Counts

34 → 3

Compiler

Compiled 1679 to 1004 computations (40.2% saved)

bsearch13.0ms (0.4%)

Steps

Iters	Range		Point
4	3312210683920468.5	5556565023280785.0	4590262224990375.0
3	-5.642794213579848e+28	-3.5066927584400546e+27	-4.747139500856354e+27

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	27	41
2	33	41
3	35	41
4	36	41
5	34	41

end1.0ms (0%)

Compiler: Compiled 30 to 19 computations (36.7% saved)

sample682.0ms (20%)

Algorithm

1×

intervals

Results

337.0ms	8000×	body	128	valid
11.0ms	278×	body	128	invalid

Compiler

Compiled 183 to 103 computations (43.7% saved)

Details

analyze153.0ms (4.5%)

sample119.0ms (3.5%)

simplify88.0ms (2.6%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series23.0ms (0.7%)

rewrite6.0ms (0.2%)

simplify108.0ms (3.2%)

prune93.0ms (2.7%)

localize6.0ms (0.2%)

series33.0ms (1%)

rewrite24.0ms (0.7%)

simplify114.0ms (3.3%)

prune84.0ms (2.5%)

localize10.0ms (0.3%)

series516.0ms (15.1%)

rewrite39.0ms (1.2%)

simplify131.0ms (3.8%)

prune157.0ms (4.6%)

localize11.0ms (0.3%)

series559.0ms (16.4%)

rewrite28.0ms (0.8%)

simplify123.0ms (3.6%)

prune134.0ms (3.9%)

regimes148.0ms (4.3%)

bsearch13.0ms (0.4%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample682.0ms (20%)

Profiling