Details

analyze838.0ms (24.8%)

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
25.9%	73.3%	0.8%	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)

sample191.0ms (5.7%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
3.0ms	82×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify66.0ms (2%)

Algorithm

1×	egg-herbie

Rules

799×	`fma-def_binary64`
661×	`fma-neg_binary64`
203×	`cancel-sign-sub-inv_binary64`
145×	`distribute-rgt-in_binary64`
99×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	30	11
3	61	11
4	129	11
5	232	11
6	397	11
7	667	11
8	1062	11
9	1355	11
10	1480	11
11	1529	11
12	1535	11
13	1540	11
14	1540	11
15	1455	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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	9.9b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
▶	6.4b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 z x))
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
✓	6.3b	(/.f64 (*.f64 y (-.f64 z x)) t)

series46.0ms (1.4%)

Counts

3 → 104

Calls

3 calls:

20.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
18.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
7.0ms	(*.f64 y (-.f64 z x))

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 92

Calls

3 calls:

6.0ms	(*.f64 y (-.f64 z x))
6.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
4.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

simplify97.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

611×	`fma-def_binary64`
609×	`times-frac_binary64`
591×	`distribute-rgt-in_binary64`
370×	`fma-neg_binary64`
158×	`associate-l_binary64`

Counts

196 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	2470
1	431	2151
2	1681	2001
3	4818	2001
4	4992	2001

prune97.0ms (2.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	137	5	142

Error

0.0b

Counts

142 → 5

Alt Table

Status	Error	Program
	9.9b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
▶	2.0b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	9.2b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
	6.4b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))
	30.0b	(+.f64 x (.f64 (sqrt.f64 (/.f64 (.f64 y (-.f64 z x)) t)) (sqrt.f64 (/.f64 (*.f64 y (-.f64 z x)) t))))

Compiler

Compiled 2492 to 707 computations (71.6% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.9b	(fma.f64 (/.f64 y t) (-.f64 z x) x)

series17.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

17.0ms

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

simplify68.0ms (2%)

Algorithm

1×	egg-herbie

Rules

546×	`distribute-rgt-neg-out_binary64`
522×	`distribute-lft-neg-out_binary64`
389×	`distribute-rgt-in_binary64`
386×	`distribute-lft-in_binary64`
294×	`times-frac_binary64`

Counts

58 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	87	635
2	197	623
3	473	623
4	2335	623
5	4674	623
6	5331	623

prune16.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	24	5	29

Error

0.0b

Counts

29 → 5

Alt Table

Status	Error	Program
	9.9b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	2.0b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
	9.2b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
▶	6.4b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))
	30.0b	(+.f64 x (.f64 (sqrt.f64 (/.f64 (.f64 y (-.f64 z x)) t)) (sqrt.f64 (/.f64 (*.f64 y (-.f64 z x)) t))))

Compiler

Compiled 399 to 140 computations (64.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (-.f64 z x))
✓	0.0b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))
✓	6.4b	(.f64 (.f64 y (-.f64 z x)) (/.f64 1 t))

series42.0ms (1.2%)

Counts

2 → 96

Calls

2 calls:

21.0ms	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))
21.0ms	(.f64 (.f64 y (-.f64 z x)) (/.f64 1 t))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-exp-log_binary64`
14×	`add-cbrt-cube_binary64`
13×	`associate-r_binary64`
12×	`prod-exp_binary64`
10×	`*-un-lft-identity_binary64`

Counts

2 → 60

Calls

2 calls:

8.0ms	(.f64 (.f64 y (-.f64 z x)) (/.f64 1 t))
4.0ms	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))

simplify80.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

634×	`distribute-rgt-in_binary64`
613×	`distribute-lft-in_binary64`
366×	`fma-def_binary64`
143×	`associate-l_binary64`
142×	`fma-neg_binary64`

Counts

156 → 105

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	136	2080
1	370	1738
2	1293	1738
3	4944	1738
4	4987	1738

prune98.0ms (2.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	164	5	169

Error

0.0b

Counts

169 → 5

Alt Table

Status	Error	Program
	9.9b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	2.0b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
▶	9.2b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
✓	6.4b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))
	30.0b	(+.f64 x (.f64 (sqrt.f64 (/.f64 (.f64 y (-.f64 z x)) t)) (sqrt.f64 (/.f64 (*.f64 y (-.f64 z x)) t))))

Compiler

Compiled 3173 to 1187 computations (62.6% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 z x))
✓	0.0b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
✓	8.9b	(/.f64 y (/.f64 t (-.f64 z x)))

series59.0ms (1.7%)

Counts

3 → 120

Calls

3 calls:

22.0ms	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
20.0ms	(/.f64 y (/.f64 t (-.f64 z x)))
17.0ms	(/.f64 t (-.f64 z x))

rewrite41.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
106×	`*-un-lft-identity_binary64`
104×	`add-sqr-sqrt_binary64`
72×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

3 → 160

Calls

3 calls:

15.0ms	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
8.0ms	(/.f64 y (/.f64 t (-.f64 z x)))
4.0ms	(/.f64 t (-.f64 z x))

simplify149.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

529×	`distribute-rgt-in_binary64`
526×	`times-frac_binary64`
479×	`fma-def_binary64`
209×	`fma-neg_binary64`
200×	`associate-/r/_binary64`

Counts

280 → 249

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	301	5064
1	696	4666
2	2435	4537
3	4826	4537
4	5007	4537

prune131.0ms (3.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	248	1	249
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	248	6	254

Error

Counts

254 → 6

Alt Table

Status	Error	Program
	9.9b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	2.0b	(fma.f64 (/.f64 y t) (-.f64 z x) x)
✓	9.2b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
✓	6.4b	(+.f64 x (.f64 (.f64 y (-.f64 z x)) (/.f64 1 t)))
	9.6b	(+.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (/.f64 t (-.f64 z x)) (cbrt.f64 y))))
	30.0b	(+.f64 x (.f64 (sqrt.f64 (/.f64 (.f64 y (-.f64 z x)) t)) (sqrt.f64 (/.f64 (*.f64 y (-.f64 z x)) t))))

Compiler

Compiled 4688 to 1173 computations (75% saved)

regimes407.0ms (12.1%)

Accuracy

Total 1.6b remaining (99%)

Threshold costs 0b (0%)

Counts

70 → 2

Compiler

Compiled 5730 to 3517 computations (38.6% saved)

bsearch19.0ms (0.6%)

Steps

Iters	Range		Point
8	-3.734431369402452e-33	-6.060352289559905e-38	-1.060814198893335e-33

Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	16	28
2	21	28
3	23	28
4	24	28
5	24	28

end1.0ms (0%)

Compiler: Compiled 24 to 12 computations (50% saved)

sample839.0ms (24.9%)

Algorithm

1×

intervals

Results

325.0ms	8000×	body	128	valid
87.0ms	2180×	body	128	invalid

Compiler

Compiled 137 to 78 computations (43.1% saved)

Details

analyze838.0ms (24.8%)

sample191.0ms (5.7%)

simplify66.0ms (2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series46.0ms (1.4%)

rewrite20.0ms (0.6%)

simplify97.0ms (2.9%)

prune97.0ms (2.9%)

localize7.0ms (0.2%)

series17.0ms (0.5%)

rewrite1.0ms (0%)

simplify68.0ms (2%)

prune16.0ms (0.5%)

localize7.0ms (0.2%)

series42.0ms (1.2%)

rewrite15.0ms (0.4%)

simplify80.0ms (2.4%)

prune98.0ms (2.9%)

localize9.0ms (0.3%)

series59.0ms (1.7%)

rewrite41.0ms (1.2%)

simplify149.0ms (4.4%)

prune131.0ms (3.9%)

regimes407.0ms (12.1%)

bsearch19.0ms (0.6%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample839.0ms (24.9%)

Profiling