Details

analyze1.3s (31.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
16.4%	83.4%	0.2%	9
21.4%	78.4%	0.2%	10
25.1%	74.7%	0.2%	11
28%	70.2%	1.9%	12
39.6%	55.8%	4.6%	13
43.9%	50.4%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample26.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
3.0ms	86×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify70.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-def_binary64`
752×	`fma-neg_binary64`
239×	`cancel-sign-sub-inv_binary64`
193×	`distribute-rgt-in_binary64`
133×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	33	11
3	64	11
4	125	11
5	238	11
6	414	11
7	791	11
8	1182	11
9	1373	11
10	1483	11
11	1532	11
12	1538	11
13	1543	11
14	1543	11
15	1458	11

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.9b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	5.8b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.8b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series17.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

17.0ms

(fma.f64 (-.f64 y x) (/.f64 z t) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (-.f64 y x) (/.f64 z t) x)

simplify70.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-neg-out_binary64`
515×	`distribute-lft-neg-out_binary64`
375×	`distribute-rgt-in_binary64`
373×	`distribute-lft-in_binary64`
270×	`times-frac_binary64`

Counts

58 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	88	635
2	194	623
3	469	623
4	2305	623
5	4632	623
6	5238	623

prune18.0ms (0.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	28	3	31
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	28	5	33

Error

0.0b

Counts

33 → 5

Alt Table

Status	Error	Program
▶	5.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	2.9b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	5.8b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
	37.9b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	35.0b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)

Compiler

Compiled 498 to 156 computations (68.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (*.f64 y z) t) x)
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	5.8b	(/.f64 (*.f64 y z) t)
✓	7.5b	(/.f64 (*.f64 z x) t)

series60.0ms (1.4%)

Counts

4 → 24

Calls

4 calls:

23.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
13.0ms	(/.f64 (*.f64 z x) t)
12.0ms	(+.f64 (/.f64 (*.f64 y z) t) x)
12.0ms	(/.f64 (*.f64 y z) t)

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
28×	`prod-diff_binary64`
28×	`add-cube-cbrt_binary64`
24×	`times-frac_binary64`

Counts

4 → 126

Calls

4 calls:

12.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
5.0ms	(+.f64 (/.f64 (*.f64 y z) t) x)
3.0ms	(/.f64 (*.f64 y z) t)
3.0ms	(/.f64 (*.f64 z x) t)

simplify94.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-def_binary64`
419×	`associate-/l/_binary64`
316×	`distribute-rgt-in_binary64`
298×	`distribute-lft-in_binary64`
193×	`cancel-sign-sub-inv_binary64`

Counts

150 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	3546
1	541	2217
2	1901	1872
3	4868	1872
4	4866	1872

prune103.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	183	2	185
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	184	6	190

Error

Counts

190 → 6

Alt Table

Status	Error	Program
▶	5.6b	(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 z (/.f64 t x)))
	5.8b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
✓	5.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 (.f64 z x) t))
✓	2.9b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	5.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 1 (/.f64 t (.f64 z x))))
	35.0b	(*.f64 (-.f64 (/.f64 y t) (/.f64 x t)) z)

Compiler

Compiled 4393 to 835 computations (81% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (/.f64 (*.f64 y z) t) x)
✓	0.0b	(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 z (/.f64 t x)))
✓	4.4b	(/.f64 z (/.f64 t x))
	5.8b	(/.f64 (*.f64 y z) t)

series35.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

22.0ms	(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 z (/.f64 t x)))
13.0ms	(/.f64 z (/.f64 t x))

rewrite81.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

408×	`times-frac_binary64`
359×	`*-un-lft-identity_binary64`
273×	`add-sqr-sqrt_binary64`
264×	`add-cube-cbrt_binary64`
176×	`prod-diff_binary64`

Counts

2 → 318

Calls

2 calls:

21.0ms	(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 z (/.f64 t x)))
4.0ms	(/.f64 z (/.f64 t x))

simplify314.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

657×	`fma-def_binary64`
430×	`associate-*r/_binary64`
365×	`associate-*l/_binary64`
269×	`associate-/r/_binary64`
222×	`associate-l_binary64`

Counts

402 → 369

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	579	23443
1	1638	12039
2	4245	11559
3	5006	11559

prune273.0ms (6.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	433	1	434
Fresh	2	1	3
Picked	0	1	1
Done	1	1	2
Total	436	4	440

Error

Counts

440 → 4

Alt Table

Status	Error	Program
	6.6b	(-.f64 (fma.f64 (/.f64 y t) z x) (/.f64 (*.f64 z x) t))
✓	2.9b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	5.6b	(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 z (/.f64 t x)))
▶	5.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 1 (/.f64 t (.f64 z x))))

Compiler

Compiled 15848 to 2791 computations (82.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 1 (/.f64 t (.f64 z x))))
✓	0.8b	(/.f64 1 (/.f64 t (*.f64 z x)))
	5.8b	(/.f64 (*.f64 y z) t)
✓	7.2b	(/.f64 t (*.f64 z x))

series54.0ms (1.3%)

Counts

3 → 84

Calls

3 calls:

24.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 1 (/.f64 t (.f64 z x))))
17.0ms	(/.f64 t (*.f64 z x))
12.0ms	(/.f64 1 (/.f64 t (*.f64 z x)))

rewrite74.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

188×	`times-frac_binary64`
181×	`*-un-lft-identity_binary64`
125×	`add-sqr-sqrt_binary64`
118×	`add-cube-cbrt_binary64`
104×	`prod-diff_binary64`

Counts

3 → 239

Calls

3 calls:

31.0ms	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 1 (/.f64 t (.f64 z x))))
5.0ms	(/.f64 1 (/.f64 t (*.f64 z x)))
3.0ms	(/.f64 t (*.f64 z x))

simplify255.0ms (6%)

Algorithm

1×	egg-herbie

Rules

639×	`fma-def_binary64`
323×	`distribute-rgt-in_binary64`
294×	`distribute-lft-in_binary64`
284×	`fma-neg_binary64`
211×	`exp-prod_binary64`

Counts

323 → 264

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	247	10007
1	586	6257
2	2005	5136
3	4597	5134
4	4983	5134
5	4981	5134
6	4741	5134

prune232.0ms (5.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	299	0	299
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	299	4	303

Error

Counts

303 → 4

Alt Table

Status	Error	Program
	6.6b	(-.f64 (fma.f64 (/.f64 y t) z x) (/.f64 (*.f64 z x) t))
✓	2.9b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
✓	5.6b	(-.f64 (+.f64 (/.f64 (*.f64 y z) t) x) (/.f64 z (/.f64 t x)))
✓	5.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) t) x) (/.f64 1 (/.f64 t (.f64 z x))))

Compiler

Compiled 10200 to 3484 computations (65.8% saved)

regimes220.0ms (5.1%)

Accuracy

Total 0.7b remaining (96.1%)

Threshold costs 0.7b (96.1%)

Counts

27 → 3

Compiler

Compiled 1881 to 1183 computations (37.1% saved)

bsearch1.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
7×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	68
1	36	68
2	46	68
3	57	68
4	63	68
5	66	68
6	67	68
7	67	68

end1.0ms (0%)

Compiler: Compiled 50 to 23 computations (54% saved)

sample877.0ms (20.5%)

Algorithm

1×

intervals

Results

319.0ms	8000×	body	128	valid
140.0ms	2112×	body	128	invalid

Compiler

Compiled 132 to 74 computations (43.9% saved)

Details

analyze1.3s (31.1%)

sample26.0ms (0.6%)

simplify70.0ms (1.6%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series17.0ms (0.4%)

rewrite1.0ms (0%)

simplify70.0ms (1.6%)

prune18.0ms (0.4%)

localize8.0ms (0.2%)

series60.0ms (1.4%)

rewrite31.0ms (0.7%)

simplify94.0ms (2.2%)

prune103.0ms (2.4%)

localize8.0ms (0.2%)

series35.0ms (0.8%)

rewrite81.0ms (1.9%)

simplify314.0ms (7.3%)

prune273.0ms (6.4%)

localize9.0ms (0.2%)

series54.0ms (1.3%)

rewrite74.0ms (1.7%)

simplify255.0ms (6%)

prune232.0ms (5.4%)

regimes220.0ms (5.1%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample877.0ms (20.5%)

Profiling