Details

analyze122.0ms (7.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
43.7%	43.7%	12.6%	7
53.1%	34.3%	12.6%	8
57.8%	23.4%	18.8%	9
63.2%	18%	18.8%	10
66%	12.1%	22%	11
68.9%	9.2%	22%	12
70.3%	6.1%	23.5%	13
71.9%	4.6%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample738.0ms (44.9%)

Results

709.0ms	8256×	body	128	valid
13.0ms	168×	body	128	invalid

Compiler

Compiled 20 to 14 computations (30% saved)

preprocess16.0ms (1%)

Algorithm

2×	egg-herbie

Rules

22×	`fma-def_binary64`
10×	`associate-r_binary64`
10×	`associate-l_binary64`
7×	`*-commutative_binary64`
6×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	28	16
2	50	16
3	87	16
4	95	16
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify15.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

13×	`fma-def_binary64`
7×	`associate-r_binary64`
7×	`associate-l_binary64`
4×	`*-commutative_binary64`
4×	`*-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	17	8
2	29	8
3	55	8
4	59	8
5	61	8

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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

5.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	5.1b	(.f64 x (+.f64 1 (.f64 y y)))
▶	5.1b	(fma.f64 x (*.f64 y y) x)

Compiler

Compiled 49 to 27 computations (44.9% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.7b	(fma.f64 x (*.f64 y y) x)

series8.0ms (0.5%)

Counts

1 → 24

Calls

6 calls:

2.0ms	(fma.f64 x (*.f64 y y) x)	x	-inf
2.0ms	(fma.f64 x (*.f64 y y) x)	x	inf
2.0ms	(fma.f64 x (*.f64 y y) x)	x	0
1.0ms	(fma.f64 x (*.f64 y y) x)	y	inf
1.0ms	(fma.f64 x (*.f64 y y) x)	y	-inf

rewrite35.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

418×	`log1p-expm1-u_binary64`
418×	`expm1-log1p-u_binary64`
266×	`unpow-prod-down_binary64`
221×	`log-prod_binary64`
148×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	99	8
2	1177	8

Stop Event

1×	node limit

Counts

1 → 40

simplify61.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
412×	`fabs-mul_binary64`
390×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
242×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	183
1	22	183
2	40	183
3	74	183
4	167	183
5	462	183
6	687	183
7	1108	183
8	1228	183
9	1363	183
10	1535	183
11	1778	183
12	2093	183
13	2465	183
14	2922	183
15	3509	183
16	4219	183

Stop Event

1×	node limit

Counts

64 → 46

prune25.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	41	5	46
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	42	6	48

Error

0.0b

Counts

48 → 6

Alt Table

Status	Error	Program
	5.1b	(.f64 x (+.f64 1 (.f64 y y)))
▶	0.1b	(fma.f64 y (*.f64 y x) x)
	37.3b	(pow.f64 (sqrt.f64 (fma.f64 x (*.f64 y y) x)) 2)
	6.3b	(pow.f64 (cbrt.f64 (fma.f64 x (*.f64 y y) x)) 3)
	31.1b	(/.f64 (-.f64 (pow.f64 (.f64 x (.f64 y y)) 2) (.f64 x x)) (fma.f64 x (.f64 y y) (neg.f64 x)))
	45.2b	(/.f64 (+.f64 (.f64 (pow.f64 x 3) (pow.f64 y 6)) (pow.f64 x 3)) (+.f64 (pow.f64 (.f64 x (.f64 y y)) 2) (-.f64 (.f64 x x) (.f64 (.f64 x (*.f64 y y)) x))))

Compiler

Compiled 731 to 287 computations (60.7% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (*.f64 y x) x)

series6.0ms (0.4%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(fma.f64 y (*.f64 y x) x)	x	-inf
1.0ms	(fma.f64 y (*.f64 y x) x)	x	inf
1.0ms	(fma.f64 y (*.f64 y x) x)	y	-inf
1.0ms	(fma.f64 y (*.f64 y x) x)	x	0
1.0ms	(fma.f64 y (*.f64 y x) x)	y	inf

rewrite33.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

443×	`log1p-expm1-u_binary64`
443×	`expm1-log1p-u_binary64`
303×	`unpow-prod-down_binary64`
252×	`log-prod_binary64`
153×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	99	8
2	1207	8

Stop Event

1×	node limit

Counts

1 → 36

simplify62.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
405×	`fabs-mul_binary64`
390×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
242×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	183
1	22	183
2	40	183
3	74	183
4	167	183
5	454	183
6	675	183
7	1096	183
8	1216	183
9	1349	183
10	1521	183
11	1764	183
12	2077	183
13	2449	183
14	2908	183
15	3483	183
16	4195	183

Stop Event

1×	node limit

Counts

60 → 42

prune23.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	42	6	48

Error

0.0b

Counts

48 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (*.f64 y x) x)
▶	5.1b	(*.f64 x (fma.f64 y y 1))
	37.3b	(pow.f64 (sqrt.f64 (fma.f64 x (*.f64 y y) x)) 2)
	6.3b	(pow.f64 (cbrt.f64 (fma.f64 x (*.f64 y y) x)) 3)
	31.1b	(/.f64 (-.f64 (pow.f64 (.f64 x (.f64 y y)) 2) (.f64 x x)) (fma.f64 x (.f64 y y) (neg.f64 x)))
	45.2b	(/.f64 (+.f64 (.f64 (pow.f64 x 3) (pow.f64 y 6)) (pow.f64 x 3)) (+.f64 (pow.f64 (.f64 x (.f64 y y)) 2) (-.f64 (.f64 x x) (.f64 (.f64 x (*.f64 y y)) x))))

Compiler

Compiled 683 to 264 computations (61.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.7b	(*.f64 x (fma.f64 y y 1))

series8.0ms (0.5%)

Counts

1 → 24

Calls

6 calls:

2.0ms	(*.f64 x (fma.f64 y y 1))	x	-inf
2.0ms	(*.f64 x (fma.f64 y y 1))	x	0
2.0ms	(*.f64 x (fma.f64 y y 1))	x	inf
1.0ms	(*.f64 x (fma.f64 y y 1))	y	-inf
1.0ms	(*.f64 x (fma.f64 y y 1))	y	inf

rewrite34.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

451×	`log1p-expm1-u_binary64`
451×	`expm1-log1p-u_binary64`
320×	`unpow-prod-down_binary64`
248×	`log-prod_binary64`
158×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	111	8
2	1236	8

Stop Event

1×	node limit

Counts

1 → 21

simplify62.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
412×	`fabs-mul_binary64`
390×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
242×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	183
1	22	183
2	40	183
3	74	183
4	167	183
5	462	183
6	687	183
7	1108	183
8	1228	183
9	1363	183
10	1535	183
11	1778	183
12	2093	183
13	2465	183
14	2922	183
15	3509	183
16	4219	183

Stop Event

1×	node limit

Counts

45 → 27

prune14.0ms (0.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	27	6	33

Error

0.0b

Counts

33 → 6

Alt Table

Status	Error	Program
	35.8b	(pow.f64 (*.f64 (hypot.f64 1 y) (sqrt.f64 x)) 2)
✓	0.1b	(fma.f64 y (*.f64 y x) x)
✓	5.1b	(*.f64 x (fma.f64 y y 1))
▶	6.3b	(pow.f64 (cbrt.f64 (fma.f64 x (*.f64 y y) x)) 3)
	31.1b	(/.f64 (-.f64 (pow.f64 (.f64 x (.f64 y y)) 2) (.f64 x x)) (fma.f64 x (.f64 y y) (neg.f64 x)))
	45.2b	(/.f64 (+.f64 (.f64 (pow.f64 x 3) (pow.f64 y 6)) (pow.f64 x 3)) (+.f64 (pow.f64 (.f64 x (.f64 y y)) 2) (-.f64 (.f64 x x) (.f64 (.f64 x (*.f64 y y)) x))))

Compiler

Compiled 398 to 194 computations (51.3% saved)

localize8.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (fma.f64 x (*.f64 y y) x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 x (*.f64 y y) x)) 3)
	4.7b	(fma.f64 x (*.f64 y y) x)

series64.0ms (3.9%)

Counts

2 → 8

Calls

12 calls:

37.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (*.f64 y y) x)) 3)	y	0
4.0ms	(cbrt.f64 (fma.f64 x (*.f64 y y) x))	y	0
3.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (*.f64 y y) x)) 3)	x	0
3.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (*.f64 y y) x)) 3)	x	-inf
3.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (*.f64 y y) x)) 3)	x	inf

rewrite41.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

578×	`log1p-expm1-u_binary64`
578×	`expm1-log1p-u_binary64`
290×	`log-prod_binary64`
117×	`expm1-udef_binary64`
117×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	159	18
2	1658	18

Stop Event

1×	node limit

Counts

2 → 68

simplify32.0ms (2%)

Algorithm

1×	egg-herbie

Rules

841×	`unswap-sqr_binary64`
767×	`fma-def_binary64`
610×	`fma-neg_binary64`
272×	`cancel-sign-sub-inv_binary64`
239×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	115
1	77	113
2	242	97
3	1038	90
4	3611	90

Stop Event

1×	node limit

Counts

76 → 79

prune53.0ms (3.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	125	6	131

Error

0.0b

Counts

131 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (*.f64 y x) x)
✓	5.1b	(*.f64 x (fma.f64 y y 1))
	37.1b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 y y)) x)
✓	6.3b	(pow.f64 (cbrt.f64 (fma.f64 x (*.f64 y y) x)) 3)
	31.1b	(/.f64 (-.f64 (pow.f64 (.f64 x (.f64 y y)) 2) (.f64 x x)) (fma.f64 x (.f64 y y) (neg.f64 x)))
	45.2b	(/.f64 (+.f64 (.f64 (pow.f64 x 3) (pow.f64 y 6)) (pow.f64 x 3)) (+.f64 (pow.f64 (.f64 x (.f64 y y)) 2) (-.f64 (.f64 x x) (.f64 (.f64 x (*.f64 y y)) x))))

Compiler

Compiled 1846 to 705 computations (61.8% saved)

regimes91.0ms (5.5%)

Accuracy

Total 0.1b remaining (59.3%)

Threshold costs 0.1b (59.3%)

Counts

19 → 1

Compiler

Compiled 1322 to 775 computations (41.4% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	6	8

Stop Event

1×

saturated

end73.0ms (4.4%)

Stop Event

1×

fuel

Compiler

Compiled 109 to 60 computations (45% saved)

Details

analyze122.0ms (7.5%)

sample738.0ms (44.9%)

preprocess16.0ms (1%)

simplify15.0ms (0.9%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series8.0ms (0.5%)

rewrite35.0ms (2.1%)

simplify61.0ms (3.7%)

prune25.0ms (1.5%)

localize4.0ms (0.2%)

series6.0ms (0.4%)

rewrite33.0ms (2%)

simplify62.0ms (3.8%)

prune23.0ms (1.4%)

localize4.0ms (0.2%)

series8.0ms (0.5%)

rewrite34.0ms (2.1%)

simplify62.0ms (3.8%)

prune14.0ms (0.9%)

localize8.0ms (0.5%)

series64.0ms (3.9%)

rewrite41.0ms (2.5%)

simplify32.0ms (2%)

prune53.0ms (3.2%)

regimes91.0ms (5.5%)

simplify4.0ms (0.2%)

end73.0ms (4.4%)

Profiling