Details

analyze13.0ms (0.2%)

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)

sample131.0ms (2%)

Algorithm

1×

intervals

Results

46.0ms

256×

body

128

valid

Compiler

Compiled 350 to 94 computations (73.1% saved)

simplify84.0ms (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

prune8.0ms (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

25.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	25.1b	(.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

▶

25.1b

(*.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)

localize36.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))
✓	0.3b	(fma.f64 1049934947/10000000000 (*.f64 x x) 1)
✓	12.6b	(.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))))))))
✓	24.7b	(/.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)))))))

series21.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

7.0ms	(/.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))))))))
4.0ms	(fma.f64 1049934947/10000000000 (*.f64 x x) 1)
4.0ms	(fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))

rewrite23.0ms (0.4%)

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:

8.0ms	(.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 1049934947/10000000000 (*.f64 x x) 1)
0.0ms	(fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))

simplify233.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

550×	`associate-l_binary64`
492×	`associate-r_binary64`
320×	`fma-def_binary64`
247×	`distribute-rgt-in_binary64`
243×	`distribute-lft-in_binary64`

Counts

131 → 184

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	8073
1	440	7191
2	1309	7182
3	4829	7182
4	4927	7182

prune463.0ms (7.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	180	4	184
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	181	4	185

Error

Counts

185 → 4

Alt Table

Status	Error	Program
	27.6b	(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x) (fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))))
▶	25.2b	(.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (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))))))) (cbrt.f64 (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))))))))) (/.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))))) (cbrt.f64 (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))))))))))
	36.1b	(+.f64 (/.f64 1307076337763/8543989815576 (pow.f64 x 5)) (+.f64 (+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3))) (/.f64 344398180852034095277/30586987988352776592 (pow.f64 x 7))))
	27.6b	(.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)))))

Compiler

Compiled 15033 to 11172 computations (25.7% saved)

localize41.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(cbrt.f64 (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)))))))
✓	12.6b	(.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (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))))))) (cbrt.f64 (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))))))))) (/.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))))) (cbrt.f64 (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))))))))))
✓	18.0b	(/.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))))) (cbrt.f64 (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))))))))
✓	23.9b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (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))))))) (cbrt.f64 (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))))))))) (/.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))))) (cbrt.f64 (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)))))))))

series42.0ms (0.7%)

Counts

4 → 48

Calls

4 calls:

12.0ms	(/.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))))) (cbrt.f64 (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))))))))
11.0ms	(.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (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))))))) (cbrt.f64 (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))))))))) (/.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))))) (cbrt.f64 (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))))))))))
11.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (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))))))) (cbrt.f64 (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))))))))) (/.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))))) (cbrt.f64 (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)))))))))
8.0ms	(cbrt.f64 (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)))))))

rewrite98.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`add-exp-log_binary64`
57×	`add-sqr-sqrt_binary64`
55×	`prod-exp_binary64`
51×	`times-frac_binary64`
41×	`add-cbrt-cube_binary64`

Counts

4 → 167

Calls

4 calls:

19.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (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))))))) (cbrt.f64 (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))))))))) (/.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))))) (cbrt.f64 (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)))))))))
13.0ms	(.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (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))))))) (cbrt.f64 (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))))))))) (/.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))))) (cbrt.f64 (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	(/.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))))) (cbrt.f64 (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	(cbrt.f64 (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)))))))

simplify655.0ms (10.2%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-def_binary64`
770×	`times-frac_binary64`
240×	`associate-r_binary64`
197×	`associate-l_binary64`
192×	`*-commutative_binary64`

Counts

215 → 321

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	370	32661
1	899	21329
2	2824	21177
3	4814	21157
4	4963	21117
5	4931	21117

prune1.8s (27.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	393	0	393
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	393	4	397

Error

Counts

397 → 4

Alt Table

Status	Error	Program
	27.6b	(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x) (fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))))
✓	25.2b	(.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (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))))))) (cbrt.f64 (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))))))))) (/.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))))) (cbrt.f64 (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))))))))))
	36.1b	(+.f64 (/.f64 1307076337763/8543989815576 (pow.f64 x 5)) (+.f64 (+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3))) (/.f64 344398180852034095277/30586987988352776592 (pow.f64 x 7))))
▶	27.6b	(.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)))))

Compiler

Compiled 58319 to 44275 computations (24.1% saved)

localize13.0ms (0.2%)

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)))
✓	21.3b	(-.f64 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1) (fma.f64 833192009/1250000000 (.f64 x x) (.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6))))

series15.0ms (0.2%)

Counts

4 → 36

Calls

4 calls:

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

rewrite14.0ms (0.2%)

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	(*.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)
0.0ms	(fma.f64 833192009/1250000000 (.f64 x x) (.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 6)))

simplify133.0ms (2.1%)

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

prune162.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	128	3	131

Error

Counts

131 → 3

Alt Table

Status	Error	Program
▶	27.6b	(.f64 x (fma.f64 (pow.f64 x 6) -9156128575487588197208397249/125000000000000000000000000000 (fma.f64 (.f64 x x) -833192009/1250000000 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1))))
✓	25.2b	(.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (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))))))) (cbrt.f64 (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))))))))) (/.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))))) (cbrt.f64 (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))))))))))
	36.1b	(+.f64 (/.f64 1307076337763/8543989815576 (pow.f64 x 5)) (+.f64 (+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3))) (/.f64 344398180852034095277/30586987988352776592 (pow.f64 x 7))))

Compiler

Compiled 3995 to 2877 computations (28% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (fma.f64 (pow.f64 x 6) -9156128575487588197208397249/125000000000000000000000000000 (fma.f64 (.f64 x x) -833192009/1250000000 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1))))
	0.0b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)
✓	11.6b	(fma.f64 (*.f64 x x) -833192009/1250000000 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1))
✓	21.4b	(fma.f64 (pow.f64 x 6) -9156128575487588197208397249/125000000000000000000000000000 (fma.f64 (*.f64 x x) -833192009/1250000000 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)))

series12.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

4.0ms

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

4.0ms

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

4.0ms

(fma.f64 (*.f64 x x) -833192009/1250000000 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

3.0ms

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

0.0ms

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

0.0ms

(fma.f64 (*.f64 x x) -833192009/1250000000 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1))

simplify99.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

528×	`cancel-sign-sub-inv_binary64`
524×	`exp-prod_binary64`
507×	`fma-neg_binary64`
368×	`associate-l_binary64`
321×	`associate-r_binary64`

Counts

78 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	93	1772
1	209	1562
2	576	1544
3	2692	1544
4	4835	1544
5	5170	1544

prune116.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Error

Counts

115 → 3

Alt Table

Status	Error	Program
✓	27.6b	(.f64 x (fma.f64 (pow.f64 x 6) -9156128575487588197208397249/125000000000000000000000000000 (fma.f64 (.f64 x x) -833192009/1250000000 (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1))))
✓	25.2b	(.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (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))))))) (cbrt.f64 (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))))))))) (/.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))))) (cbrt.f64 (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))))))))))
	36.1b	(+.f64 (/.f64 1307076337763/8543989815576 (pow.f64 x 5)) (+.f64 (+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3))) (/.f64 344398180852034095277/30586987988352776592 (pow.f64 x 7))))

Compiler

Compiled 2803 to 2004 computations (28.5% saved)

regimes306.0ms (4.8%)

Accuracy

Total 0.2b remaining (93%)

Threshold costs 0.2b (93%)

Counts

54 → 3

Compiler

Compiled 5410 to 3800 computations (29.8% saved)

bsearch78.0ms (1.2%)

Steps

Iters	Range		Point
9	0.021388322851141887	1493.8169658115035	1.4497235596354414
8	-228.05070153915534	-0.006081273583464981	-1.4368502133983208

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	39	70
1	48	70
2	47	70

end1.0ms (0%)

Compiler: Compiled 49 to 38 computations (22.4% saved)

sample1.9s (28.8%)

Algorithm

1×

intervals

Results

1.4s

8000×

body

128

valid

Compiler

Compiled 396 to 217 computations (45.2% saved)

Details

analyze13.0ms (0.2%)

sample131.0ms (2%)

simplify84.0ms (1.3%)

prune8.0ms (0.1%)

localize36.0ms (0.6%)

series21.0ms (0.3%)

rewrite23.0ms (0.4%)

simplify233.0ms (3.6%)

prune463.0ms (7.2%)

localize41.0ms (0.6%)

series42.0ms (0.7%)

rewrite98.0ms (1.5%)

simplify655.0ms (10.2%)

prune1.8s (27.3%)

localize13.0ms (0.2%)

series15.0ms (0.2%)

rewrite14.0ms (0.2%)

simplify133.0ms (2.1%)

prune162.0ms (2.5%)

localize12.0ms (0.2%)

series12.0ms (0.2%)

rewrite6.0ms (0.1%)

simplify99.0ms (1.5%)

prune116.0ms (1.8%)

regimes306.0ms (4.8%)

bsearch78.0ms (1.2%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.9s (28.8%)

Profiling