Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample127.0ms (2.9%)

Algorithm

1×

intervals

Results

11.0ms	62×	body	1024	valid
7.0ms	143×	body	128	valid
4.0ms	28×	body	512	valid
2.0ms	11×	body	2048	valid
1.0ms	12×	body	256	valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify88.0ms (2%)

Algorithm

1×	egg-herbie

Rules

859×	`fma-neg_binary64`
770×	`fma-def_binary64`
322×	`div-sub_binary64`
178×	`associate-/l*_binary64`
150×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	16	19
2	22	19
3	34	19
4	57	19
5	91	19
6	178	19
7	277	19
8	643	19
9	788	19
10	1024	19
11	1265	19
12	1242	19
13	1248	19
14	1246	19
15	1248	19
16	1250	19
17	1260	19
18	1260	19
19	1171	19

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

27.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	27.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x 1))
✓	0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
✓	2.8b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series8.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.0ms	(/.f64 x (+.f64 x 1))

rewrite220.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Rules

1322×	`*-un-lft-identity_binary64`
1012×	`times-frac_binary64`
869×	`add-sqr-sqrt_binary64`
612×	`prod-diff_binary64`
533×	`add-cube-cbrt_binary64`

Counts

3 → 783

Calls

3 calls:

44.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
6.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
4.0ms	(/.f64 x (+.f64 x 1))

simplify915.0ms (21%)

Algorithm

1×	egg-herbie

Rules

654×	`fma-neg_binary64`
367×	`unsub-neg_binary64`
299×	`fma-udef_binary64`
213×	`sub-neg_binary64`
202×	`associate-+r-_binary64`

Counts

819 → 619

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	545	54602
1	1290	31108
2	3043	22839
3	4323	22837
4	4983	22837
5	4991	22837
6	4742	22837

prune653.0ms (15%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	616	3	619
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	616	4	620

Error

Counts

620 → 4

Alt Table

Status	Error	Program
	33.7b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
	33.8b	(neg.f64 (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))))
✓	27.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
▶	29.9b	(+.f64 1 (*.f64 x (+.f64 3 x)))

Compiler

Compiled 30382 to 22391 computations (26.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 3 x))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(*.f64 x (+.f64 3 x))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 25

Calls

1 calls:

4.0ms

(*.f64 x (+.f64 3 x))

simplify87.0ms (2%)

Algorithm

1×	egg-herbie

Rules

982×	`fma-def_binary64`
428×	`unswap-sqr_binary64`
372×	`distribute-rgt-out_binary64`
345×	`+-commutative_binary64`
343×	`associate-+r+_binary64`

Counts

37 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	48	335
1	122	303
2	392	303
3	1110	303
4	2468	303
5	3561	303
6	4612	303
7	4910	303
8	4853	303

prune18.0ms (0.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	33	4	37

Error

Counts

37 → 4

Alt Table

Status	Error	Program
▶	33.7b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
	33.8b	(neg.f64 (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))))
✓	27.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
✓	29.9b	(+.f64 1 (*.f64 x (+.f64 3 x)))

Compiler

Compiled 491 to 352 computations (28.3% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
✓	0.3b	(/.f64 3 (pow.f64 x 3))
✓	0.4b	(/.f64 1 (*.f64 x x))
✓	7.0b	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))

series12.0ms (0.3%)

Counts

4 → 36

Calls

4 calls:

4.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
3.0ms	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
3.0ms	(/.f64 3 (pow.f64 x 3))
2.0ms	(/.f64 1 (*.f64 x x))

rewrite80.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

178×	`*-un-lft-identity_binary64`
136×	`times-frac_binary64`
101×	`add-sqr-sqrt_binary64`
96×	`add-cube-cbrt_binary64`
78×	`prod-diff_binary64`

Counts

4 → 245

Calls

4 calls:

29.0ms	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
19.0ms	(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3)))
4.0ms	(/.f64 3 (pow.f64 x 3))
3.0ms	(/.f64 1 (*.f64 x x))

simplify181.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

508×	`unswap-sqr_binary64`
388×	`cancel-sign-sub-inv_binary64`
372×	`fma-neg_binary64`
185×	`associate-l_binary64`
185×	`associate-/r*_binary64`

Counts

281 → 274

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	298	8270
1	610	6566
2	2500	5026
3	4684	5026
4	4880	5026

prune219.0ms (5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	274	4	278

Error

Counts

278 → 4

Alt Table

Status	Error	Program
✓	33.7b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
▶	33.8b	(neg.f64 (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))))
✓	27.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
✓	29.9b	(+.f64 1 (*.f64 x (+.f64 3 x)))

Compiler

Compiled 9349 to 6482 computations (30.7% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (pow.f64 x 3))
✓	0.3b	(*.f64 3 (/.f64 1 x))
✓	0.4b	(/.f64 1 (pow.f64 x 2))
✓	7.0b	(+.f64 (*.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))

series10.0ms (0.2%)

Counts

4 → 15

Calls

4 calls:

4.0ms	(+.f64 (*.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))
3.0ms	(/.f64 1 (pow.f64 x 3))
2.0ms	(/.f64 1 (pow.f64 x 2))
1.0ms	(*.f64 3 (/.f64 1 x))

rewrite37.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`times-frac_binary64`
61×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
54×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

4 → 188

Calls

4 calls:

13.0ms	(+.f64 (*.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))
5.0ms	(*.f64 3 (/.f64 1 x))
4.0ms	(/.f64 1 (pow.f64 x 3))
3.0ms	(/.f64 1 (pow.f64 x 2))

simplify133.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-neg_binary64`
443×	`associate-/l*_binary64`
339×	`unswap-sqr_binary64`
281×	`log-prod_binary64`
276×	`associate-/l/_binary64`

Counts

203 → 232

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	172	2198
1	346	2025
2	1085	1812
3	3333	1718
4	4163	1709
5	4927	1709
6	5062	1709

prune177.0ms (4.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	232	0	232
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	232	4	236

Error

Counts

236 → 4

Alt Table

Status	Error	Program
✓	33.7b	(-.f64 (/.f64 -3 x) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 3 (pow.f64 x 3))))
✓	33.8b	(neg.f64 (+.f64 (.f64 3 (/.f64 1 x)) (+.f64 (.f64 3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2)))))
✓	27.6b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
✓	29.9b	(+.f64 1 (*.f64 x (+.f64 3 x)))

Compiler

Compiled 6095 to 5042 computations (17.3% saved)

regimes75.0ms (1.7%)

Accuracy

Total 0.0b remaining (19.1%)

Threshold costs 0.0b (19.1%)

Counts

27 → 3

Compiler

Compiled 772 to 612 computations (20.7% saved)

bsearch32.0ms (0.7%)

Steps

Iters	Range		Point
9	14.555179136679113	1898572075.0696535	11243.776937313149
10	-231595.90953896684	-2.3457489550793586e-6	-10559.50745449947

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
9×	`sub-neg_binary64`
6×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	55
1	38	55
2	51	55
3	69	55
4	80	55
5	85	55
6	86	55
7	83	55

end1.0ms (0%)

Compiler: Compiled 38 to 28 computations (26.3% saved)

sample1.2s (28.1%)

Algorithm

1×

intervals

Results

374.0ms	1933×	body	1024	valid
323.0ms	4337×	body	128	valid
140.0ms	1011×	body	512	valid
59.0ms	233×	body	2048	valid
45.0ms	486×	body	256	valid

Compiler

Compiled 113 to 86 computations (23.9% saved)

Details

analyze5.0ms (0.1%)

sample127.0ms (2.9%)

simplify88.0ms (2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series8.0ms (0.2%)

rewrite220.0ms (5.1%)

simplify915.0ms (21%)

prune653.0ms (15%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify87.0ms (2%)

prune18.0ms (0.4%)

localize15.0ms (0.4%)

series12.0ms (0.3%)

rewrite80.0ms (1.8%)

simplify181.0ms (4.2%)

prune219.0ms (5%)

localize12.0ms (0.3%)

series10.0ms (0.2%)

rewrite37.0ms (0.9%)

simplify133.0ms (3.1%)

prune177.0ms (4.1%)

regimes75.0ms (1.7%)

bsearch32.0ms (0.7%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.2s (28.1%)

Profiling