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)

sample2.0s (54.9%)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 524 to 140 computations (73.3% saved)

simplify64.0ms (1.7%)

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

30.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	30.0b	(.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)
▶	30.0b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))

Status

Error

Program

30.0b

(*.f64 (/.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)

▶

30.0b

(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))

Compiler

Compiled 704 to 274 computations (61.1% saved)

localize30.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(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))))
✓	0.2b	(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))))
✓	13.6b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (*.f64 x x) 7715471019/10000000000 1))))))))
✓	29.5b	(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (fma.f64 2532017/5000000000 (pow.f64 x 8) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (.f64 x x) 7715471019/10000000000 1)))))))

series19.0ms (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 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))))
3.0ms	(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))))

rewrite62.0ms (1.7%)

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:

60.0ms	(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))))
60.0ms	(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))))
60.0ms	(.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))))))))
59.0ms	(/.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	223
1	802	223
2	4756	223

simplify80.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

441×	`associate-/r*_binary64`
440×	`times-frac_binary64`
436×	`fma-def_binary64`
428×	`cancel-sign-sub-inv_binary64`
244×	`fma-neg_binary64`

Counts

114 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	792
1	283	784
2	698	772
3	1877	772
4	4440	772
5	4954	772
6	4988	772

prune205.0ms (5.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	122	3	125

Error

Counts

125 → 3

Alt Table

Status	Error	Program
▶	29.6b	(+.f64 (+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3))) (/.f64 1307076337763/8543989815576 (pow.f64 x 5)))
	33.8b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -833192009/1250000000 x))
	30.0b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (+.f64 (.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 6384 to 4774 computations (25.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3))) (/.f64 1307076337763/8543989815576 (pow.f64 x 5)))
✓	0.0b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
✓	0.3b	(/.f64 1307076337763/8543989815576 (pow.f64 x 5))
✓	0.4b	(/.f64 600041/2386628 (pow.f64 x 3))

series16.0ms (0.4%)

Counts

4 → 24

Calls

4 calls:

6.0ms	(/.f64 1307076337763/8543989815576 (pow.f64 x 5))
4.0ms	(+.f64 (+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3))) (/.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))

rewrite91.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

290×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
164×	`egg-rr`
164×	`log1p-expm1-u_binary64`
164×	`expm1-log1p-u_binary64`

Counts

4 → 164

Calls

4 calls:

88.0ms	(+.f64 (+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3))) (/.f64 1307076337763/8543989815576 (pow.f64 x 5)))
88.0ms	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
88.0ms	(/.f64 1307076337763/8543989815576 (pow.f64 x 5))
88.0ms	(/.f64 600041/2386628 (pow.f64 x 3))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	49
1	341	43
2	4564	43
3	4764	43

simplify106.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

724×	`unswap-sqr_binary64`
510×	`sqr-pow_binary64`
503×	`associate-/l/_binary64`
501×	`associate-/r*_binary64`
356×	`times-frac_binary64`

Counts

188 → 171

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	321
1	50	321
2	91	321
3	149	321
4	263	321
5	691	321
6	2517	321
7	3895	321
8	3862	321
9	4136	321
10	4451	321
11	4668	321
12	4877	321

prune127.0ms (3.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	171	3	174

Error

Counts

174 → 3

Alt Table

Status	Error	Program
✓	29.6b	(+.f64 (+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3))) (/.f64 1307076337763/8543989815576 (pow.f64 x 5)))
	33.8b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -833192009/1250000000 x))
▶	30.0b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (+.f64 (.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 4299 to 3423 computations (20.4% saved)

localize31.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(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))))
✓	0.3b	(*.f64 2532017/5000000000 (pow.f64 x 8))
✓	13.6b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (+.f64 (.f64 2532017/5000000000 (pow.f64 x 8)) (fma.f64 36322091/5000000000 (pow.f64 x 6) (fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (.f64 x x) 1))))) (fma.f64 1789971/5000000000 (pow.f64 x 12) (fma.f64 (pow.f64 x 10) 1665589/2000000000 (fma.f64 (pow.f64 x 8) 70002721/5000000000 (fma.f64 (pow.f64 x 6) 694555761/10000000000 (fma.f64 (pow.f64 x 4) 2909738639/10000000000 (fma.f64 (.f64 x x) 7715471019/10000000000 1))))))))
✓	29.5b	(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (+.f64 (.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)))))))

series16.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

5.0ms

(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (+.f64 (*.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 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (+.f64 (*.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

(*.f64 2532017/5000000000 (pow.f64 x 8))

rewrite50.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

373×	`log1p-expm1-u_binary64`
373×	`expm1-log1p-u_binary64`
365×	`add-cbrt-cube_binary64`
363×	`add-log-exp_binary64`
362×	`add-exp-log_binary64`

Counts

3 → 45

Calls

3 calls:

48.0ms

(*.f64 2532017/5000000000 (pow.f64 x 8))

48.0ms

(*.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (+.f64 (*.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))))))))

48.0ms

(/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (+.f64 (*.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	39	172
1	832	172
2	5049	172

simplify53.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

708×	`times-frac_binary64`
698×	`unswap-sqr_binary64`
636×	`fma-def_binary64`
630×	`associate-l_binary64`
441×	`associate-/r*_binary64`

Counts

69 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	68	408
1	185	408
2	450	400
3	1193	396
4	3662	396
5	5808	396

prune147.0ms (3.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	105	3	108

Error

Counts

108 → 3

Alt Table

Status	Error	Program
✓	29.6b	(+.f64 (+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3))) (/.f64 1307076337763/8543989815576 (pow.f64 x 5)))
▶	33.8b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -833192009/1250000000 x))
✓	30.0b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (+.f64 (.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 5331 to 3998 computations (25% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)
✓	17.3b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -833192009/1250000000 x))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -833192009/1250000000 x))
3.0ms	(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)

rewrite52.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

836×	`log1p-expm1-u_binary64`
836×	`expm1-log1p-u_binary64`
103×	`prod-diff_binary64`
100×	`add-sqr-sqrt_binary64`
95×	`add-cbrt-cube_binary64`

Counts

2 → 49

Calls

2 calls:

50.0ms	(fma.f64 (pow.f64 x 3) -833192009/1250000000 x)
50.0ms	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -833192009/1250000000 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	214	23
2	2153	23
3	5050	23

simplify125.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

976×	`fma-neg_binary64`
541×	`distribute-rgt-neg-in_binary64`
418×	`distribute-lft-neg-in_binary64`
416×	`unswap-sqr_binary64`
405×	`cancel-sign-sub-inv_binary64`

Counts

73 → 58

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	264
1	43	260
2	94	228
3	237	228
4	511	228
5	1281	228
6	1983	228
7	3739	228
8	4307	228
9	4647	228
10	4957	228
11	4997	228
12	4831	228

prune38.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	58	3	61

Error

Counts

61 → 3

Alt Table

Status	Error	Program
✓	29.6b	(+.f64 (+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3))) (/.f64 1307076337763/8543989815576 (pow.f64 x 5)))
✓	33.8b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 5) (fma.f64 (pow.f64 x 3) -833192009/1250000000 x))
✓	30.0b	(.f64 x (/.f64 (fma.f64 1789971/10000000000 (pow.f64 x 10) (+.f64 (.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 983 to 761 computations (22.6% saved)

regimes145.0ms (3.9%)

Accuracy

Total 0.0b remaining (37.2%)

Threshold costs 0.0b (37.2%)

Counts

35 → 3

Compiler

Compiled 2442 to 1524 computations (37.6% saved)

bsearch43.0ms (1.2%)

Steps

Iters	Range		Point
8	5.659586023480387	4512.790750182248	695.5042817586066
1	-250417786.47604093	-16852857.676696677	-64932296.98620179

Compiler

Compiled 2 to 1 computations (50% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
11×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	304
1	92	304
2	90	304

end133.0ms (3.6%)

Compiler: Compiled 502 to 209 computations (58.4% saved)

Details

analyze10.0ms (0.3%)

sample2.0s (54.9%)

simplify64.0ms (1.7%)

prune9.0ms (0.2%)

localize30.0ms (0.8%)

series19.0ms (0.5%)

rewrite62.0ms (1.7%)

simplify80.0ms (2.2%)

prune205.0ms (5.5%)

localize8.0ms (0.2%)

series16.0ms (0.4%)

rewrite91.0ms (2.4%)

simplify106.0ms (2.8%)

prune127.0ms (3.4%)

localize31.0ms (0.8%)

series16.0ms (0.4%)

rewrite50.0ms (1.3%)

simplify53.0ms (1.4%)

prune147.0ms (3.9%)

localize7.0ms (0.2%)

series7.0ms (0.2%)

rewrite52.0ms (1.4%)

simplify125.0ms (3.3%)

prune38.0ms (1%)

regimes145.0ms (3.9%)

bsearch43.0ms (1.2%)

simplify6.0ms (0.2%)

end133.0ms (3.6%)

Profiling