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)

sample1.8s (59.7%)

Results

1.7s

8256×

body

128

valid

Compiler

Compiled 524 to 140 computations (73.3% saved)

simplify67.0ms (2.2%)

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

prune7.0ms (0.2%)

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

30.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	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 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)

localize33.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (*.f64 x x) 7715471019/10000000000 1)
✓	0.2b	(fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))
✓	14.2b	(.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)))))))

series17.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(/.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)))))))
5.0ms	(.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))))))))
3.0ms	(fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))
2.0ms	(fma.f64 (*.f64 x x) 7715471019/10000000000 1)

rewrite57.0ms (1.9%)

Algorithm

2×	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 → 62

Calls

4 calls:

55.0ms	(fma.f64 (*.f64 x x) 7715471019/10000000000 1)
55.0ms	(fma.f64 106015151/2500000000 (pow.f64 x 4) (fma.f64 1049934947/10000000000 (*.f64 x x) 1))
55.0ms	(.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))))))))
55.0ms	(/.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	188
1	802	188
2	4756	188
0	0	0
1	0	0

simplify73.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

110 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	668
1	206	636
2	497	628
3	1290	624
4	3393	624
5	4730	624
6	4954	624

prune149.0ms (4.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	3	104

Error

Counts

104 → 3

Alt Table

Status	Error	Program
▶	31.2b	(.f64 x (fma.f64 (pow.f64 x 6) -9156128575487588197208397249/125000000000000000000000000000 (fma.f64 x (.f64 x -833192009/1250000000) (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1))))
	32.4b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
✓	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 5282 to 3948 computations (25.3% saved)

localize11.0ms (0.4%)

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 x (.f64 x -833192009/1250000000) (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1))))
✓	0.0b	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)
✓	0.1b	(*.f64 x -833192009/1250000000)
✓	25.3b	(fma.f64 (pow.f64 x 6) -9156128575487588197208397249/125000000000000000000000000000 (fma.f64 x (*.f64 x -833192009/1250000000) (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)))

series12.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(.f64 x (fma.f64 (pow.f64 x 6) -9156128575487588197208397249/125000000000000000000000000000 (fma.f64 x (.f64 x -833192009/1250000000) (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1))))
4.0ms	(fma.f64 (pow.f64 x 6) -9156128575487588197208397249/125000000000000000000000000000 (fma.f64 x (*.f64 x -833192009/1250000000) (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)))
3.0ms	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)
1.0ms	(*.f64 x -833192009/1250000000)

rewrite74.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

551×	`log-prod_binary64`
239×	`expm1-udef_binary64`
239×	`log1p-udef_binary64`
201×	`log-pow_binary64`
140×	`add-sqr-sqrt_binary64`

Counts

4 → 94

Calls

4 calls:

72.0ms	(.f64 x (fma.f64 (pow.f64 x 6) -9156128575487588197208397249/125000000000000000000000000000 (fma.f64 x (.f64 x -833192009/1250000000) (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1))))
72.0ms	(fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)
72.0ms	(*.f64 x -833192009/1250000000)
72.0ms	(fma.f64 (pow.f64 x 6) -9156128575487588197208397249/125000000000000000000000000000 (fma.f64 x (*.f64 x -833192009/1250000000) (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	59
1	310	59
2	3046	59
3	4998	59
0	0	0
1	0	0

simplify116.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

715×	`fma-def_binary64`
676×	`distribute-rgt-neg-in_binary64`
670×	`associate-l_binary64`
473×	`unswap-sqr_binary64`
460×	`cancel-sign-sub-inv_binary64`

Counts

142 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	519
1	126	511
2	296	495
3	882	483
4	2834	483
5	4367	483
6	4923	483
7	4993	483
8	4935	483

prune99.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	123	3	126

Error

Counts

126 → 3

Alt Table

Status	Error	Program
✓	31.2b	(.f64 x (fma.f64 (pow.f64 x 6) -9156128575487588197208397249/125000000000000000000000000000 (fma.f64 x (.f64 x -833192009/1250000000) (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1))))
▶	32.4b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
✓	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 2771 to 2103 computations (24.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series7.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

4.0ms	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
3.0ms	(/.f64 600041/2386628 (pow.f64 x 3))

rewrite58.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

916×	`prod-diff_binary64`
184×	`expm1-udef_binary64`
184×	`log1p-udef_binary64`
105×	`add-sqr-sqrt_binary64`
103×	`log1p-expm1-u_binary64`

Counts

2 → 80

Calls

2 calls:

57.0ms	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
57.0ms	(/.f64 600041/2386628 (pow.f64 x 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	215	18
2	2774	18
3	4964	18
0	0	0
1	0	0

simplify104.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1081×	`associate-/l*_binary64`
914×	`associate-*l/_binary64`
600×	`associate-/r/_binary64`
362×	`unswap-sqr_binary64`
322×	`sqr-pow_binary64`

Counts

92 → 84

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	132
1	30	132
2	51	132
3	82	132
4	142	132
5	366	132
6	1278	132
7	1590	132
8	1604	132
9	1734	132
10	1888	132
11	2045	132
12	4438	132
13	4734	132
14	4865	132
15	4802	132

prune44.0ms (1.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	84	3	87

Error

Counts

87 → 3

Alt Table

Status	Error	Program
✓	31.2b	(.f64 x (fma.f64 (pow.f64 x 6) -9156128575487588197208397249/125000000000000000000000000000 (fma.f64 x (.f64 x -833192009/1250000000) (fma.f64 3321371254951887171/12500000000000000000 (pow.f64 x 4) 1))))
✓	32.4b	(+.f64 (/.f64 1/2 x) (/.f64 600041/2386628 (pow.f64 x 3)))
✓	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 1370 to 1068 computations (22% saved)

regimes99.0ms (3.3%)

Accuracy

Total 0.0b remaining (46.1%)

Threshold costs 0.0b (46.1%)

Counts

25 → 3

Compiler

Compiled 1356 to 688 computations (49.3% saved)

bsearch38.0ms (1.3%)

Steps

Iters	Range		Point
5	4.708349371313006	3356319889.007298	851925.2708437147
4	-26048.69894505976	-0.016894010236394218	-10715.910557922929

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	294
1	90	294
2	88	294

end140.0ms (4.6%)

Compiler: Compiled 486 to 196 computations (59.7% saved)

Details

analyze10.0ms (0.3%)

sample1.8s (59.7%)

simplify67.0ms (2.2%)

prune7.0ms (0.2%)

localize33.0ms (1.1%)

series17.0ms (0.6%)

rewrite57.0ms (1.9%)

simplify73.0ms (2.4%)

prune149.0ms (4.9%)

localize11.0ms (0.4%)

series12.0ms (0.4%)

rewrite74.0ms (2.4%)

simplify116.0ms (3.8%)

prune99.0ms (3.3%)

localize5.0ms (0.2%)

series7.0ms (0.2%)

rewrite58.0ms (1.9%)

simplify104.0ms (3.4%)

prune44.0ms (1.4%)

regimes99.0ms (3.3%)

bsearch38.0ms (1.3%)

simplify5.0ms (0.2%)

end140.0ms (4.6%)

Profiling