Details

analyze3.6s (51.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0%	100%	0%	14

Compiler

Compiled 175 to 47 computations (73.1% saved)

sample2.0s (28.5%)

Results

1.9s

8256×

body

128

valid

Compiler

Compiled 349 to 93 computations (73.4% saved)

simplify67.0ms (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 (0.1%)

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)

localize33.0ms (0.5%)

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 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1)))
✓	13.6b	(.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)))))))

series20.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

7.0ms	(.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))))))))
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)))))))
4.0ms	(fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1)))
2.0ms	(fma.f64 (*.f64 x x) 7715471019/10000000000 1)

rewrite19.0ms (0.3%)

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))))))))
2.0ms	(/.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 (*.f64 x x) 7715471019/10000000000 1)
0.0ms	(fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1)))

simplify210.0ms (3%)

Algorithm

1×	egg-herbie

Rules

548×	`associate-l_binary64`
481×	`associate-r_binary64`
362×	`fma-def_binary64`
245×	`distribute-rgt-in_binary64`
237×	`distribute-lft-in_binary64`

Counts

131 → 184

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	8196
1	458	7294
2	1333	7285
3	4924	7285
4	4967	7285

prune436.0ms (6.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

Counts

185 → 2

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))))))))
▶	30.7b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

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))))))))

▶

30.7b

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

Compiler

Compiled 14695 to 10922 computations (25.7% saved)

localize5.0ms (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)))
✓	0.4b	(/.f64 600041/2386628 (pow.f64 x 3))

series6.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

3.0ms	(/.f64 600041/2386628 (pow.f64 x 3))
3.0ms	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

rewrite32.0ms (0.5%)

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:

20.0ms	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
4.0ms	(/.f64 600041/2386628 (pow.f64 x 3))

simplify74.0ms (1.1%)

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

prune113.0ms (1.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	112	2	114

Error

Counts

114 → 2

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))))))))
✓	30.7b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))

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))))))))

✓

30.7b

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

Compiler

Compiled 1892 to 1466 computations (22.5% saved)

regimes192.0ms (2.8%)

Accuracy

Total 0.0b remaining (13.5%)

Threshold costs 0.0b (13.5%)

Counts

44 → 3

Compiler

Compiled 2998 to 1968 computations (34.4% saved)

bsearch38.0ms (0.5%)

Steps

Iters	Range		Point
2	322044.7526831057	2775960.6415720866	525492.669122914
5	-23652935634.332455	-2076402.2840280668	-2933610.2141926717

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	111
1	59	111
2	58	111

end141.0ms (2%)

Compiler: Compiled 229 to 174 computations (24% saved)

Details

analyze3.6s (51.4%)

sample2.0s (28.5%)

simplify67.0ms (1%)

prune7.0ms (0.1%)

localize33.0ms (0.5%)

series20.0ms (0.3%)

rewrite19.0ms (0.3%)

simplify210.0ms (3%)

prune436.0ms (6.3%)

localize5.0ms (0.1%)

series6.0ms (0.1%)

rewrite32.0ms (0.5%)

simplify74.0ms (1.1%)

prune113.0ms (1.6%)

regimes192.0ms (2.8%)

bsearch38.0ms (0.5%)

simplify7.0ms (0.1%)

end141.0ms (2%)

Profiling