Details

analyze3.3s (42.8%)

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)

sample1.9s (24.3%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 349 to 93 computations (73.4% saved)

simplify66.0ms (0.9%)

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

prune9.0ms (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

30.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	30.3b	(.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))))))))
▶	30.3b	(.f64 (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1049934947/10000000000 (.f64 x x))) (.f64 106015151/2500000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 36322091/5000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2532017/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1789971/10000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 7715471019/10000000000 (.f64 x x))) (.f64 2909738639/10000000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 694555761/10000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 70002721/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1665589/2000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 1789971/10000000000) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x))))) x)

Status

Error

Program

30.3b

(*.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))))))))

▶

30.3b

(*.f64 (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (*.f64 1049934947/10000000000 (*.f64 x x))) (*.f64 106015151/2500000000 (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 36322091/5000000000 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)))) (*.f64 2532017/5000000000 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (*.f64 1789971/10000000000 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (*.f64 7715471019/10000000000 (*.f64 x x))) (*.f64 2909738639/10000000000 (*.f64 (*.f64 x x) (*.f64 x x)))) (*.f64 694555761/10000000000 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)))) (*.f64 70002721/5000000000 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (*.f64 1665589/2000000000 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)))) (*.f64 (*.f64 2 1789971/10000000000) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x)) (*.f64 x x))))) x)

Compiler

Compiled 704 to 274 computations (61.1% saved)

localize40.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 7715471019/10000000000 (.f64 x x))
✓	0.2b	(.f64 36322091/5000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))
✓	12.6b	(.f64 (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1049934947/10000000000 (.f64 x x))) (.f64 106015151/2500000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 36322091/5000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2532017/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1789971/10000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 7715471019/10000000000 (.f64 x x))) (.f64 2909738639/10000000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 694555761/10000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 70002721/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1665589/2000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 1789971/10000000000) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x))))) x)
✓	29.7b	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1049934947/10000000000 (.f64 x x))) (.f64 106015151/2500000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 36322091/5000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2532017/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1789971/10000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 7715471019/10000000000 (.f64 x x))) (.f64 2909738639/10000000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 694555761/10000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 70002721/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1665589/2000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 1789971/10000000000) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (*.f64 x x)))))

series26.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

11.0ms	(.f64 (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1049934947/10000000000 (.f64 x x))) (.f64 106015151/2500000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 36322091/5000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2532017/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1789971/10000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 7715471019/10000000000 (.f64 x x))) (.f64 2909738639/10000000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 694555761/10000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 70002721/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1665589/2000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 1789971/10000000000) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x))))) x)
9.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1049934947/10000000000 (.f64 x x))) (.f64 106015151/2500000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 36322091/5000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2532017/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1789971/10000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 7715471019/10000000000 (.f64 x x))) (.f64 2909738639/10000000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 694555761/10000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 70002721/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1665589/2000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 1789971/10000000000) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (*.f64 x x)))))
3.0ms	(.f64 36322091/5000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))
2.0ms	(.f64 7715471019/10000000000 (.f64 x x))

rewrite247.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-cbrt-cube_binary64`
69×	`add-exp-log_binary64`
64×	`pow1_binary64`
47×	`cbrt-unprod_binary64`
47×	`prod-exp_binary64`

Counts

4 → 137

Calls

4 calls:

73.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1049934947/10000000000 (.f64 x x))) (.f64 106015151/2500000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 36322091/5000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2532017/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1789971/10000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 7715471019/10000000000 (.f64 x x))) (.f64 2909738639/10000000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 694555761/10000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 70002721/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1665589/2000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 1789971/10000000000) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (*.f64 x x)))))
67.0ms	(.f64 (/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 1049934947/10000000000 (.f64 x x))) (.f64 106015151/2500000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 36322091/5000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 2532017/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1789971/10000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 7715471019/10000000000 (.f64 x x))) (.f64 2909738639/10000000000 (.f64 (.f64 x x) (.f64 x x)))) (.f64 694555761/10000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))) (.f64 70002721/5000000000 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 1665589/2000000000 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)))) (.f64 (.f64 2 1789971/10000000000) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x)) (.f64 x x))))) x)
56.0ms	(.f64 36322091/5000000000 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)))
5.0ms	(.f64 7715471019/10000000000 (.f64 x x))

simplify242.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

474×	`cancel-sign-sub-inv_binary64`
370×	`associate-r_binary64`
352×	`associate-l_binary64`
342×	`fma-neg_binary64`
166×	`*-commutative_binary64`

Counts

185 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	315	12684
1	756	8543
2	3124	8007
3	4921	8007

prune483.0ms (6.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	228	3	231
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	230	3	233

Error

Counts

233 → 3

Alt Table

Status	Error	Program
	30.3b	(expm1.f64 (log1p.f64 (.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 (pow.f64 x 8) 2532017/5000000000 (fma.f64 (pow.f64 x 6) 36322091/5000000000 (fma.f64 (pow.f64 x 4) 106015151/2500000000 (fma.f64 (.f64 x x) 1049934947/10000000000 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 1/2 x)
	33.3b	(-.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))))

Compiler

Compiled 43666 to 12916 computations (70.4% saved)

localize2.0ms (0%)

prune5.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
▶	30.3b	(expm1.f64 (log1p.f64 (.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 (pow.f64 x 8) 2532017/5000000000 (fma.f64 (pow.f64 x 6) 36322091/5000000000 (fma.f64 (pow.f64 x 4) 106015151/2500000000 (fma.f64 (.f64 x x) 1049934947/10000000000 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 1/2 x)
	33.3b	(-.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))))

Compiler

Compiled 166 to 127 computations (23.5% saved)

localize34.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (*.f64 x x) 1049934947/10000000000 1)
✓	0.2b	(fma.f64 (pow.f64 x 6) 36322091/5000000000 (fma.f64 (pow.f64 x 4) 106015151/2500000000 (fma.f64 (*.f64 x x) 1049934947/10000000000 1)))
✓	12.6b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 (pow.f64 x 8) 2532017/5000000000 (fma.f64 (pow.f64 x 6) 36322091/5000000000 (fma.f64 (pow.f64 x 4) 106015151/2500000000 (fma.f64 (.f64 x x) 1049934947/10000000000 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))))))))
✓	29.7b	(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 (pow.f64 x 8) 2532017/5000000000 (fma.f64 (pow.f64 x 6) 36322091/5000000000 (fma.f64 (pow.f64 x 4) 106015151/2500000000 (fma.f64 (.f64 x x) 1049934947/10000000000 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 (pow.f64 x 8) 2532017/5000000000 (fma.f64 (pow.f64 x 6) 36322091/5000000000 (fma.f64 (pow.f64 x 4) 106015151/2500000000 (fma.f64 (.f64 x x) 1049934947/10000000000 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 (pow.f64 x 8) 2532017/5000000000 (fma.f64 (pow.f64 x 6) 36322091/5000000000 (fma.f64 (pow.f64 x 4) 106015151/2500000000 (fma.f64 (.f64 x x) 1049934947/10000000000 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 (pow.f64 x 6) 36322091/5000000000 (fma.f64 (pow.f64 x 4) 106015151/2500000000 (fma.f64 (*.f64 x x) 1049934947/10000000000 1)))
3.0ms	(fma.f64 (*.f64 x x) 1049934947/10000000000 1)

rewrite19.0ms (0.2%)

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 (pow.f64 x 8) 2532017/5000000000 (fma.f64 (pow.f64 x 6) 36322091/5000000000 (fma.f64 (pow.f64 x 4) 106015151/2500000000 (fma.f64 (.f64 x x) 1049934947/10000000000 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 (pow.f64 x 8) 2532017/5000000000 (fma.f64 (pow.f64 x 6) 36322091/5000000000 (fma.f64 (pow.f64 x 4) 106015151/2500000000 (fma.f64 (.f64 x x) 1049934947/10000000000 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 (pow.f64 x 6) 36322091/5000000000 (fma.f64 (pow.f64 x 4) 106015151/2500000000 (fma.f64 (*.f64 x x) 1049934947/10000000000 1)))
0.0ms	(fma.f64 (*.f64 x x) 1049934947/10000000000 1)

simplify196.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

554×	`associate-l_binary64`
471×	`associate-r_binary64`
362×	`fma-def_binary64`
245×	`distribute-rgt-in_binary64`
237×	`distribute-lft-in_binary64`

Counts

131 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	207	8196
1	457	7294
2	1329	7285
3	4916	7285
4	4959	7285

prune382.0ms (4.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	181	3	184

Error

Counts

184 → 3

Alt Table

Status	Error	Program
✓	30.3b	(expm1.f64 (log1p.f64 (.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 (pow.f64 x 8) 2532017/5000000000 (fma.f64 (pow.f64 x 6) 36322091/5000000000 (fma.f64 (pow.f64 x 4) 106015151/2500000000 (fma.f64 (.f64 x x) 1049934947/10000000000 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 1/2 x)
▶	33.3b	(-.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))))

Compiler

Compiled 14897 to 11165 computations (25.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7)))
✓	0.1b	(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))
✓	0.1b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x)
✓	24.0b	(-.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))))

series18.0ms (0.2%)

Counts

4 → 36

Calls

4 calls:

6.0ms	(fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7)))
4.0ms	(-.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))))
4.0ms	(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))
4.0ms	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x)

rewrite12.0ms (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:

4.0ms	(*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7))
3.0ms	(-.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))))
0.0ms	(fma.f64 833192009/1250000000 (pow.f64 x 3) (*.f64 9156128575487588197208397249/125000000000000000000000000000 (pow.f64 x 7)))
0.0ms	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) x)

simplify124.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

874×	`fma-neg_binary64`
633×	`times-frac_binary64`
600×	`associate-r_binary64`
389×	`fma-def_binary64`
339×	`distribute-lft-in_binary64`

Counts

115 → 122

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	142	2229
1	264	2018
2	793	1831
3	3426	1774
4	4426	1759
5	5632	1759

prune136.0ms (1.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	122	3	125

Error

Counts

125 → 3

Alt Table

Status	Error	Program
✓	30.3b	(expm1.f64 (log1p.f64 (.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 (pow.f64 x 8) 2532017/5000000000 (fma.f64 (pow.f64 x 6) 36322091/5000000000 (fma.f64 (pow.f64 x 4) 106015151/2500000000 (fma.f64 (.f64 x x) 1049934947/10000000000 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 1/2 x)
✓	33.3b	(-.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))))

Compiler

Compiled 3519 to 2790 computations (20.7% saved)

regimes273.0ms (3.5%)

Accuracy

Total 0.0b remaining (57.3%)

Threshold costs 0.0b (57.3%)

Counts

53 → 3

Compiler

Compiled 6454 to 3750 computations (41.9% saved)

bsearch67.0ms (0.9%)

Steps

Iters	Range		Point
5	3.916820032061989e-9	72095225371.52528	70429503.43634991
9	-22244517359.392338	-59.19600534667539	-92476053.96525763

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	144
1	56	144
2	55	144

end145.0ms (1.9%)

Compiler: Compiled 289 to 219 computations (24.2% saved)

Details

analyze3.3s (42.8%)

sample1.9s (24.3%)

simplify66.0ms (0.9%)

prune9.0ms (0.1%)

localize40.0ms (0.5%)

series26.0ms (0.3%)

rewrite247.0ms (3.2%)

simplify242.0ms (3.1%)

prune483.0ms (6.2%)

localize2.0ms (0%)

prune5.0ms (0.1%)

localize34.0ms (0.4%)

series20.0ms (0.3%)

rewrite19.0ms (0.2%)

simplify196.0ms (2.5%)

prune382.0ms (4.9%)

localize12.0ms (0.2%)

series18.0ms (0.2%)

rewrite12.0ms (0.2%)

simplify124.0ms (1.6%)

prune136.0ms (1.7%)

regimes273.0ms (3.5%)

bsearch67.0ms (0.9%)

simplify4.0ms (0%)

end145.0ms (1.9%)

Profiling