Details

analyze10.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
81.2%	18.7%	0%	6
100%	0%	0%	7

Compiler

Compiled 175 to 47 computations (73.1% saved)

sample134.0ms (4.2%)

Algorithm

1×

intervals

Results

42.0ms

256×

body

128

valid

Compiler

Compiled 350 to 94 computations (73.1% saved)

simplify68.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

755×	`unswap-sqr_binary64`
705×	`fma-def_binary64`
691×	`distribute-rgt-out_binary64`
576×	`+-commutative_binary64`
488×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	46	256
1	133	150
2	549	101
3	2427	90
4	3705	84
5	4529	84
6	4874	84
7	5887	84

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

30.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.4b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))

Status

Error

Program

▶

30.4b

(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))

Compiler

Compiled 356 to 182 computations (48.9% saved)

localize33.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (*.f64 x x) 7715471019/10000000000 1)
✓	0.1b	(fma.f64 1049934947/10000000000 (*.f64 x x) 1)
✓	15.0b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
✓	29.9b	(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (.f64 x x) 7715471019/10000000000 1)))))))

series17.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (.f64 x x) 7715471019/10000000000 1)))))))
6.0ms	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
3.0ms	(fma.f64 1049934947/10000000000 (*.f64 x x) 1)
3.0ms	(fma.f64 (*.f64 x x) 7715471019/10000000000 1)

rewrite21.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

5.0ms	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
5.0ms	(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (.f64 x x) 7715471019/10000000000 1)))))))
0.0ms	(fma.f64 1049934947/10000000000 (*.f64 x x) 1)
0.0ms	(fma.f64 (*.f64 x x) 7715471019/10000000000 1)

simplify271.0ms (8.4%)

Algorithm

1×	egg-herbie

Rules

533×	`associate-l_binary64`
482×	`associate-r_binary64`
301×	`fma-def_binary64`
236×	`associate-*r/_binary64`
211×	`associate-*l/_binary64`

Counts

131 → 176

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	7935
1	437	7066
2	1287	7058
3	4538	7058
4	4758	7058
5	4997	7058
6	4901	7058

prune375.0ms (11.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	174	2	176
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	174	3	177

Error

Counts

177 → 3

Alt Table

Status	Error	Program
▶	31.1b	(.f64 x (-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (.f64 x x) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))))
	31.6b	(/.f64 1/2 x)
✓	30.4b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))

Compiler

Compiled 14219 to 10558 computations (25.7% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)
✓	0.1b	(fma.f64 833192009/1250000000 (.f64 x x) (.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))
✓	0.1b	(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))
✓	26.6b	(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (.f64 x x) (.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))))

series16.0ms (0.5%)

Counts

4 → 36

Calls

4 calls:

5.0ms	(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (.f64 x x) (.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))))
4.0ms	(fma.f64 833192009/1250000000 (.f64 x x) (.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))
3.0ms	(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))
3.0ms	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`
9×	`prod-diff_binary64`

Counts

4 → 79

Calls

4 calls:

6.0ms	(fma.f64 833192009/1250000000 (.f64 x x) (.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))
4.0ms	(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))
3.0ms	(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (.f64 x x) (.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))))
0.0ms	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)

simplify143.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

615×	`fma-neg_binary64`
406×	`fma-def_binary64`
336×	`distribute-rgt-in_binary64`
335×	`distribute-lft-in_binary64`
334×	`exp-prod_binary64`

Counts

115 → 127

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	143	2226
1	260	2014
2	802	1804
3	2777	1749
4	4342	1734
5	4956	1734
6	4860	1734

prune136.0ms (4.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	127	3	130

Error

Counts

130 → 3

Alt Table

Status	Error	Program
✓	31.1b	(.f64 x (-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (.f64 x x) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))))
▶	31.6b	(/.f64 1/2 x)
✓	30.4b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))

Compiler

Compiled 3872 to 2781 computations (28.2% saved)

localize2.0ms (0.1%)

prune4.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	31.1b	(.f64 x (-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (.f64 x x) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))))
✓	31.6b	(/.f64 1/2 x)
✓	30.4b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))

Compiler

Compiled 85 to 64 computations (24.7% saved)

regimes159.0ms (4.9%)

Accuracy

Total 0.7b remaining (98.6%)

Threshold costs 0.7b (98.6%)

Counts

38 → 2

Compiler

Compiled 2516 to 1574 computations (37.4% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 174 to 46 computations (73.6% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary64`
11×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	349
1	105	349
2	103	349

end2.0ms (0.1%)

Compiler: Compiled 238 to 93 computations (60.9% saved)

sample1.8s (55.5%)

Algorithm

1×

intervals

Results

1.4s

8000×

body

128

valid

Compiler

Compiled 499 to 205 computations (58.9% saved)

Details

analyze10.0ms (0.3%)

sample134.0ms (4.2%)

simplify68.0ms (2.1%)

prune7.0ms (0.2%)

localize33.0ms (1%)

series17.0ms (0.5%)

rewrite21.0ms (0.6%)

simplify271.0ms (8.4%)

prune375.0ms (11.6%)

localize12.0ms (0.4%)

series16.0ms (0.5%)

rewrite17.0ms (0.5%)

simplify143.0ms (4.4%)

prune136.0ms (4.2%)

localize2.0ms (0.1%)

prune4.0ms (0.1%)

regimes159.0ms (4.9%)

bsearch3.0ms (0.1%)

simplify8.0ms (0.2%)

end2.0ms (0.1%)

sample1.8s (55.5%)

Profiling