Details

analyze11.0ms (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)

sample125.0ms (2.8%)

Algorithm

1×

intervals

Results

41.0ms

256×

body

128

valid

Compiler

Compiled 350 to 94 computations (73.1% saved)

simplify66.0ms (1.5%)

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

32.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	32.4b	(.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 (+.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

32.4b

(*.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 (+.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)

localize42.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 7715471019/10000000000 (.f64 x x))
✓	0.4b	(.f64 1049934947/10000000000 (.f64 x x))
✓	15.5b	(.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)
✓	31.8b	(/.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)))))

series24.0ms (0.5%)

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)))))
8.0ms	(.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)
4.0ms	(.f64 1049934947/10000000000 (.f64 x x))
2.0ms	(.f64 7715471019/10000000000 (.f64 x x))

rewrite184.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
21×	`associate-l_binary64`
21×	`add-cbrt-cube_binary64`

Counts

4 → 111

Calls

4 calls:

69.0ms	(/.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)))))
62.0ms	(.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)
4.0ms	(.f64 7715471019/10000000000 (.f64 x x))
4.0ms	(.f64 1049934947/10000000000 (.f64 x x))

simplify258.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

604×	`fma-neg_binary64`
402×	`cancel-sign-sub-inv_binary64`
284×	`associate-r_binary64`
261×	`associate-l_binary64`
221×	`distribute-rgt-out_binary64`

Counts

159 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	12333
1	729	8804
2	2851	7758
3	4928	7758
4	5145	7758

prune404.0ms (9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	212	3	215
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	214	3	217

Error

Counts

217 → 3

Alt Table

Status	Error	Program
	44.4b	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) (/.f64 600041/2386628 (pow.f64 x 4))) x)
	32.4b	(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))))))))))
▶	28.7b	(+.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 40643 to 12179 computations (70% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
✓	0.1b	(/.f64 344398180852034095277/30586987988352776592 (pow.f64 x 7))
✓	0.2b	(/.f64 1307076337763/8543989815576 (pow.f64 x 5))
✓	0.5b	(/.f64 600041/2386628 (pow.f64 x 3))

series13.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

4.0ms	(/.f64 344398180852034095277/30586987988352776592 (pow.f64 x 7))
3.0ms	(/.f64 1307076337763/8543989815576 (pow.f64 x 5))
3.0ms	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
3.0ms	(/.f64 600041/2386628 (pow.f64 x 3))

rewrite43.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`times-frac_binary64`
74×	`*-un-lft-identity_binary64`
68×	`add-sqr-sqrt_binary64`
68×	`add-cube-cbrt_binary64`
36×	`unpow-prod-down_binary64`

Counts

4 → 190

Calls

4 calls:

23.0ms	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
4.0ms	(/.f64 344398180852034095277/30586987988352776592 (pow.f64 x 7))
4.0ms	(/.f64 600041/2386628 (pow.f64 x 3))
3.0ms	(/.f64 1307076337763/8543989815576 (pow.f64 x 5))

simplify116.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

834×	`fma-def_binary64`
461×	`associate-/l*_binary64`
396×	`associate-*l/_binary64`
392×	`associate-/l/_binary64`
182×	`associate-/r*_binary64`

Counts

202 → 222

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	2747
1	498	2648
2	1563	2554
3	4597	2554
4	5117	2554

prune205.0ms (4.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	222	3	225

Error

Counts

225 → 3

Alt Table

Status	Error	Program
	44.4b	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) (/.f64 600041/2386628 (pow.f64 x 4))) x)
▶	32.4b	(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))))))))))
✓	28.7b	(+.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 6471 to 5226 computations (19.2% saved)

localize35.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))
✓	0.3b	(fma.f64 (*.f64 x x) 1049934947/10000000000 1)
✓	15.5b	(.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))))))))
✓	31.8b	(/.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 (0.5%)

Counts

4 → 48

Calls

4 calls:

8.0ms	(.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 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))
3.0ms	(fma.f64 (*.f64 x x) 1049934947/10000000000 1)

rewrite20.0ms (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:

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 (*.f64 x x) 1049934947/10000000000 1)
0.0ms	(fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))

simplify221.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

564×	`associate-l_binary64`
476×	`associate-r_binary64`
321×	`fma-def_binary64`
249×	`distribute-rgt-in_binary64`
241×	`distribute-lft-in_binary64`

Counts

131 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	8073
1	443	7191
2	1315	7182
3	4848	7182
4	4920	7182

prune278.0ms (6.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	140	3	143

Error

Counts

143 → 3

Alt Table

Status	Error	Program
▶	44.4b	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) (/.f64 600041/2386628 (pow.f64 x 4))) x)
✓	32.4b	(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))))))))))
✓	28.7b	(+.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 10698 to 8014 computations (25.1% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 600041/2386628 (pow.f64 x 4)))
✓	0.3b	(/.f64 600041/2386628 (pow.f64 x 4))
✓	0.3b	(/.f64 1/2 (*.f64 x x))
✓	19.0b	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) (/.f64 600041/2386628 (pow.f64 x 4))) x)

series23.0ms (0.5%)

Counts

4 → 36

Calls

4 calls:

13.0ms	(/.f64 600041/2386628 (pow.f64 x 4))
4.0ms	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) (/.f64 600041/2386628 (pow.f64 x 4))) x)
4.0ms	(+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 600041/2386628 (pow.f64 x 4)))
2.0ms	(/.f64 1/2 (*.f64 x x))

rewrite41.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
27×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`
16×	`add-exp-log_binary64`

Counts

4 → 116

Calls

4 calls:

15.0ms	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) (/.f64 600041/2386628 (pow.f64 x 4))) x)
12.0ms	(+.f64 (/.f64 1/2 (*.f64 x x)) (/.f64 600041/2386628 (pow.f64 x 4)))
6.0ms	(/.f64 600041/2386628 (pow.f64 x 4))
3.0ms	(/.f64 1/2 (*.f64 x x))

simplify93.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

396×	`associate-*l/_binary64`
376×	`associate-/r*_binary64`
365×	`associate-*r/_binary64`
347×	`times-frac_binary64`
273×	`fma-def_binary64`

Counts

152 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	2285
1	366	2128
2	1163	2031
3	4729	2031
4	4930	2031

prune103.0ms (2.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	157	3	160

Error

Counts

160 → 3

Alt Table

Status	Error	Program
✓	44.4b	(.f64 (+.f64 (/.f64 1/2 (.f64 x x)) (/.f64 600041/2386628 (pow.f64 x 4))) x)
✓	32.4b	(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))))))))))
✓	28.7b	(+.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 3343 to 2254 computations (32.6% saved)

regimes395.0ms (8.8%)

Accuracy

Total 0.0b remaining (19.6%)

Threshold costs 0.0b (19.6%)

Counts

83 → 3

Compiler

Compiled 6344 to 3564 computations (43.8% saved)

bsearch34.0ms (0.8%)

Steps

Iters	Range		Point
4	2501299.6914299624	1877876605.2803416	105231599.08440648
3	-30221.195823059028	-490.97785935396	-849.2628000532544

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	145
1	81	145
2	80	145

end2.0ms (0.1%)

Compiler: Compiled 101 to 80 computations (20.8% saved)

sample1.7s (38%)

Algorithm

1×

intervals

Results

1.4s

8000×

body

128

valid

Compiler

Compiled 376 to 204 computations (45.7% saved)

Details

analyze11.0ms (0.2%)

sample125.0ms (2.8%)

simplify66.0ms (1.5%)

prune9.0ms (0.2%)

localize42.0ms (0.9%)

series24.0ms (0.5%)

rewrite184.0ms (4.1%)

simplify258.0ms (5.7%)

prune404.0ms (9%)

localize13.0ms (0.3%)

series13.0ms (0.3%)

rewrite43.0ms (1%)

simplify116.0ms (2.6%)

prune205.0ms (4.6%)

localize35.0ms (0.8%)

series20.0ms (0.5%)

rewrite20.0ms (0.4%)

simplify221.0ms (4.9%)

prune278.0ms (6.2%)

localize7.0ms (0.2%)

series23.0ms (0.5%)

rewrite41.0ms (0.9%)

simplify93.0ms (2.1%)

prune103.0ms (2.3%)

regimes395.0ms (8.8%)

bsearch34.0ms (0.8%)

simplify4.0ms (0.1%)

end2.0ms (0.1%)

sample1.7s (38%)

Profiling