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)

sample1.9s (55%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 524 to 140 computations (73.3% saved)

simplify65.0ms (1.9%)

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 (0.2%)

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

31.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	31.3b	(.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))))))))
▶	31.3b	(.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

31.3b

(*.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))))))))

▶

31.3b

(*.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)

localize37.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 2909738639/10000000000 (.f64 (.f64 x x) (.f64 x x)))
✓	0.3b	(.f64 106015151/2500000000 (.f64 (.f64 x x) (.f64 x x)))
✓	15.9b	(.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)
✓	30.7b	(/.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)))))

series22.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

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)))))
7.0ms	(.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)
3.0ms	(.f64 2909738639/10000000000 (.f64 (.f64 x x) (.f64 x x)))
3.0ms	(.f64 106015151/2500000000 (.f64 (.f64 x x) (.f64 x x)))

rewrite162.0ms (4.6%)

Algorithm

1×	batch-egg-rewrite

Rules

506×	`log1p-expm1-u_binary64`
506×	`expm1-log1p-u_binary64`
424×	`prod-diff_binary64`
178×	`unpow-prod-down_binary64`
177×	`fma-def_binary64`

Counts

4 → 57

Calls

4 calls:

159.0ms	(.f64 2909738639/10000000000 (.f64 (.f64 x x) (.f64 x x)))
159.0ms	(.f64 106015151/2500000000 (.f64 (.f64 x x) (.f64 x x)))
159.0ms	(.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)
159.0ms	(/.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)))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	373
1	1067	293
2	4877	293
3	5148	293

simplify103.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

636×	`fma-def_binary64`
466×	`times-frac_binary64`
441×	`associate-/r*_binary64`
428×	`cancel-sign-sub-inv_binary64`
393×	`unswap-sqr_binary64`

Counts

105 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	576
1	191	576
2	464	568
3	1235	564
4	3299	564
5	4636	564
6	4951	564
7	4992	564
8	4910	564

prune208.0ms (5.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	89	3	92

Error

Counts

92 → 3

Alt Table

Status	Error	Program
▶	28.7b	(/.f64 1/2 x)
	34.1b	(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)
	31.3b	(.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))))))))

Compiler

Compiled 9044 to 4093 computations (54.7% 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
✓	28.7b	(/.f64 1/2 x)
	34.1b	(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)
▶	31.3b	(.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))))))))

Compiler

Compiled 140 to 105 computations (25% saved)

localize31.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))
✓	0.3b	(fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))
✓	15.9b	(.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 (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)))))))

series18.0ms (0.5%)

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))))))))
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)))))))
3.0ms	(fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))
3.0ms	(fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))

rewrite62.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

357×	`log1p-expm1-u_binary64`
357×	`expm1-log1p-u_binary64`
351×	`add-cbrt-cube_binary64`
349×	`add-log-exp_binary64`
348×	`add-exp-log_binary64`

Counts

4 → 66

Calls

4 calls:

57.0ms	(fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))
57.0ms	(fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))
57.0ms	(.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))))))))
57.0ms	(/.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)))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	195
1	802	195
2	4756	195

simplify74.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

744×	`fma-def_binary64`
466×	`times-frac_binary64`
441×	`associate-/r*_binary64`
428×	`cancel-sign-sub-inv_binary64`
393×	`unswap-sqr_binary64`

Counts

114 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	718
1	217	690
2	522	682
3	1345	678
4	3483	678
5	4657	678
6	5192	678

prune205.0ms (5.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	110	3	113

Error

Counts

113 → 3

Alt Table

Status	Error	Program
✓	28.7b	(/.f64 1/2 x)
▶	34.1b	(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)
✓	31.3b	(.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))))))))

Compiler

Compiled 5653 to 4224 computations (25.3% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)

rewrite73.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

493×	`log1p-expm1-u_binary64`
493×	`expm1-log1p-u_binary64`
281×	`unpow-prod-down_binary64`
223×	`log-prod_binary64`
208×	`prod-diff_binary64`

Counts

1 → 37

Calls

1 calls:

73.0ms

(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	126	8
2	1280	8
3	4890	8
4	5011	8

simplify163.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

1705×	`fma-def_binary64`
865×	`fma-neg_binary64`
818×	`unswap-sqr_binary64`
615×	`sqr-pow_binary64`
528×	`cube-prod_binary64`

Counts

49 → 42

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	105
1	23	105
2	59	87
3	147	87
4	298	87
5	774	87
6	1120	87
7	1710	87
8	3217	87
9	4164	87
10	4277	87
11	4261	87
12	4044	87
13	3304	87
14	3939	87
15	4360	87
16	4810	87
17	4770	87

prune26.0ms (0.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	42	3	45

Error

Counts

45 → 3

Alt Table

Status	Error	Program
✓	28.7b	(/.f64 1/2 x)
✓	34.1b	(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)
✓	31.3b	(.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))))))))

Compiler

Compiled 577 to 444 computations (23.1% saved)

regimes148.0ms (4.2%)

Accuracy

Total 0.3b remaining (95.8%)

Threshold costs 0.3b (95.8%)

Counts

33 → 3

Compiler

Compiled 2548 to 1614 computations (36.7% saved)

bsearch33.0ms (0.9%)

Steps

Iters	Range		Point
5	8529296.80080126	1000941826.3793063	82315534.54281782
2	-76677341211940270.0	-4072972.39924222	-1581231300.6377075

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	97
1	48	97
2	47	97

end115.0ms (3.3%)

Compiler: Compiled 212 to 158 computations (25.5% saved)

Details

analyze10.0ms (0.3%)

sample1.9s (55%)

simplify65.0ms (1.9%)

prune9.0ms (0.2%)

localize37.0ms (1.1%)

series22.0ms (0.6%)

rewrite162.0ms (4.6%)

simplify103.0ms (2.9%)

prune208.0ms (5.9%)

localize2.0ms (0%)

prune5.0ms (0.1%)

localize31.0ms (0.9%)

series18.0ms (0.5%)

rewrite62.0ms (1.8%)

simplify74.0ms (2.1%)

prune205.0ms (5.8%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite73.0ms (2.1%)

simplify163.0ms (4.6%)

prune26.0ms (0.7%)

regimes148.0ms (4.2%)

bsearch33.0ms (0.9%)

simplify5.0ms (0.1%)

end115.0ms (3.3%)

Profiling