Details

analyze25.0ms (0.4%)

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)

sample3.4s (56.1%)

Results

3.2s

8256×

body

128

valid

Compiler

Compiled 524 to 140 computations (73.3% saved)

simplify80.0ms (1.3%)

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

prune13.0ms (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

30.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.0b	(.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))))))))

Status

Error

Program

▶

30.0b

(*.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))))))))

Compiler

Compiled 356 to 182 computations (48.9% saved)

localize60.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (*.f64 x x) 7715471019/10000000000 1)
✓	0.2b	(fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))
✓	14.2b	(.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))))))))
✓	29.5b	(/.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)))))))

series28.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

10.0ms	(/.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)))))))
9.0ms	(.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	(fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))
4.0ms	(fma.f64 (*.f64 x x) 7715471019/10000000000 1)

rewrite34.0ms (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:

12.0ms	(.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))))))))
4.0ms	(/.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)))))))
1.0ms	(fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))
1.0ms	(fma.f64 (*.f64 x x) 7715471019/10000000000 1)

simplify308.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

549×	`associate-l_binary64`
491×	`associate-r_binary64`
322×	`fma-def_binary64`
249×	`distribute-rgt-in_binary64`
241×	`distribute-lft-in_binary64`

Counts

131 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	8073
1	442	7191
2	1315	7182
3	4846	7182
4	4918	7182

prune769.0ms (12.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	178	3	181

Error

Counts

181 → 3

Alt Table

Status	Error	Program
▶	31.2b	(.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)))))
✓	30.0b	(.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))))))))
	32.4b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

Compiler

Compiled 14492 to 10767 computations (25.7% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)
✓	0.1b	(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))
✓	0.1b	(fma.f64 833192009/1250000000 (.f64 x x) (.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))
✓	25.3b	(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (.f64 x x) (.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))))

series26.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

10.0ms	(fma.f64 833192009/1250000000 (.f64 x x) (.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))
6.0ms	(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))
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))))
5.0ms	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)

rewrite24.0ms (0.4%)

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:

7.0ms	(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))
6.0ms	(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (.f64 x x) (.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))))
1.0ms	(fma.f64 833192009/1250000000 (.f64 x x) (.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))
1.0ms	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)

simplify202.0ms (3.3%)

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

prune232.0ms (3.8%)

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
✓	31.2b	(.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)))))
✓	30.0b	(.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))))))))
▶	32.4b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

Compiler

Compiled 3884 to 2791 computations (28.1% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
✓	0.3b	(/.f64 600041/2386628 (pow.f64 x 3))

series11.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

6.0ms	(/.f64 600041/2386628 (pow.f64 x 3))
5.0ms	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

rewrite47.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`times-frac_binary64`
40×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
34×	`add-cube-cbrt_binary64`
13×	`fma-def_binary64`

Counts

2 → 96

Calls

2 calls:

33.0ms	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
6.0ms	(/.f64 600041/2386628 (pow.f64 x 3))

simplify100.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

683×	`associate-l_binary64`
353×	`associate-/l*_binary64`
342×	`associate-*r/_binary64`
342×	`associate-*l/_binary64`
272×	`associate-/l/_binary64`

Counts

108 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1319
1	242	1280
2	965	1242
3	4706	1242
4	4947	1242

prune116.0ms (1.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	112	3	115

Error

Counts

115 → 3

Alt Table

Status	Error	Program
✓	31.2b	(.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)))))
✓	30.0b	(.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))))))))
✓	32.4b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

Compiler

Compiled 1912 to 1481 computations (22.5% saved)

regimes189.0ms (3.1%)

Accuracy

Total 0.0b remaining (37.6%)

Threshold costs 0.0b (37.6%)

Counts

25 → 3

Compiler

Compiled 1398 to 722 computations (48.4% saved)

bsearch42.0ms (0.7%)

Steps

Iters	Range		Point
1	4.708349371313006	3356319889.007298	122552.17526243192
4	-26048.69894505976	-0.016894010236394218	-10715.910557922929

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	122
1	56	122
2	55	122

end314.0ms (5.2%)

Compiler: Compiled 265 to 201 computations (24.2% saved)

Details

analyze25.0ms (0.4%)

sample3.4s (56.1%)

simplify80.0ms (1.3%)

prune13.0ms (0.2%)

localize60.0ms (1%)

series28.0ms (0.5%)

rewrite34.0ms (0.6%)

simplify308.0ms (5.1%)

prune769.0ms (12.7%)

localize21.0ms (0.3%)

series26.0ms (0.4%)

rewrite24.0ms (0.4%)

simplify202.0ms (3.3%)

prune232.0ms (3.8%)

localize9.0ms (0.1%)

series11.0ms (0.2%)

rewrite47.0ms (0.8%)

simplify100.0ms (1.7%)

prune116.0ms (1.9%)

regimes189.0ms (3.1%)

bsearch42.0ms (0.7%)

simplify6.0ms (0.1%)

end314.0ms (5.2%)

Profiling