Details

analyze194.0ms (3.9%)

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)

sample1.3s (25.8%)

Results

1.2s	8256×	body	128	valid
31.0ms	185×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify16.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	17	8
2	24	8
3	47	8
4	43	8
5	45	8
6	43	8

prune4.0ms (0.1%)

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

4.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.8b	(*.f64 x (fma.f64 y y 1))

Compiler

Compiled 31 to 19 computations (38.7% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.5b	(*.f64 x (fma.f64 y y 1))

series19.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

19.0ms

(*.f64 x (fma.f64 y y 1))

rewrite92.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

833×	`log1p-udef_binary64`
451×	`log1p-expm1-u_binary64`
451×	`expm1-log1p-u_binary64`
318×	`unpow-prod-down_binary64`
248×	`log-prod_binary64`

Counts

1 → 21

Calls

1 calls:

91.0ms

(*.f64 x (fma.f64 y y 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	111	8
2	1192	8
3	4791	8
4	6195	8
0	0	0
1	0	0

simplify182.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1104×	`sqr-pow_binary64`
673×	`cube-prod_binary64`
663×	`fabs-mul_binary64`
628×	`pow-sqr_binary64`
311×	`cube-mult_binary64`

Counts

45 → 27

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	183
1	21	183
2	37	183
3	56	183
4	132	183
5	315	183
6	398	183
7	638	183
8	673	183
9	783	183
10	901	183
11	1066	183
12	1226	183
13	1453	183
14	1786	183
15	2180	183
16	2738	183
17	3422	183
18	3647	183
19	3912	183
20	4004	183
21	4038	183
22	4059	183
23	4997	183
24	4857	183

prune33.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	22	5	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	5	28

Error

2.5b

Counts

28 → 5

Alt Table

Status	Error	Program
	22.0b	x
▶	4.8b	(fma.f64 x (*.f64 y y) x)
	43.1b	(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 y y 1)) 3))
	32.1b	(pow.f64 (*.f64 (sqrt.f64 x) (hypot.f64 1 y)) 2)
	6.1b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 y y 1))) 3)

Compiler

Compiled 318 to 197 computations (38.1% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.5b	(fma.f64 x (*.f64 y y) x)

series17.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

17.0ms

(fma.f64 x (*.f64 y y) x)

rewrite109.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

764×	`log1p-udef_binary64`
418×	`log1p-expm1-u_binary64`
418×	`expm1-log1p-u_binary64`
264×	`unpow-prod-down_binary64`
221×	`log-prod_binary64`

Counts

1 → 40

Calls

1 calls:

107.0ms

(fma.f64 x (*.f64 y y) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	99	8
2	1095	8
3	4680	8
4	6047	8
0	0	0
1	0	0

simplify170.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1104×	`sqr-pow_binary64`
673×	`cube-prod_binary64`
663×	`fabs-mul_binary64`
628×	`pow-sqr_binary64`
311×	`cube-mult_binary64`

Counts

64 → 46

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	183
1	21	183
2	37	183
3	56	183
4	132	183
5	315	183
6	398	183
7	638	183
8	673	183
9	783	183
10	901	183
11	1066	183
12	1226	183
13	1453	183
14	1786	183
15	2180	183
16	2738	183
17	3422	183
18	3647	183
19	3912	183
20	4004	183
21	4038	183
22	4059	183
23	4997	183
24	4857	183

prune42.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	43	8	51

Error

2.5b

Counts

51 → 8

Alt Table

Status	Error	Program
	6.8b	(.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (.f64 y y) x))) 2) 3) (cbrt.f64 (fma.f64 x (*.f64 y y) x)))
✓	4.8b	(fma.f64 x (*.f64 y y) x)
	22.0b	x
	33.2b	(/.f64 (-.f64 (pow.f64 (.f64 x (.f64 y y)) 2) (.f64 x x)) (-.f64 (.f64 x (*.f64 y y)) x))
	43.8b	(/.f64 (+.f64 (pow.f64 (.f64 x (.f64 y y)) 3) (pow.f64 x 3)) (+.f64 (pow.f64 (.f64 x (.f64 y y)) 2) (-.f64 (.f64 x x) (.f64 (.f64 x (.f64 y y)) x))))
	43.1b	(cbrt.f64 (pow.f64 (*.f64 x (fma.f64 y y 1)) 3))
	32.1b	(pow.f64 (*.f64 (sqrt.f64 x) (hypot.f64 1 y)) 2)
▶	6.1b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 y y 1))) 3)

Compiler

Compiled 773 to 304 computations (60.7% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (*.f64 x (fma.f64 y y 1)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 y y 1))) 3)
	4.5b	(*.f64 x (fma.f64 y y 1))

series1.7s (33.4%)

Counts

2 → 48

Calls

2 calls:

983.0ms	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 y y 1))) 3)
695.0ms	(cbrt.f64 (*.f64 x (fma.f64 y y 1)))

rewrite115.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

623×	`log1p-expm1-u_binary64`
623×	`expm1-log1p-u_binary64`
325×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Counts

2 → 67

Calls

2 calls:

112.0ms	(cbrt.f64 (*.f64 x (fma.f64 y y 1)))
112.0ms	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 y y 1))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	160	18
2	1650	18
3	4987	18
4	4912	18
0	0	0
1	0	0

simplify136.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

524×	`fma-neg_binary64`
449×	`cancel-sign-sub-inv_binary64`
292×	`unswap-sqr_binary64`
247×	`fma-def_binary64`
234×	`prod-exp_binary64`

Counts

115 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	1450
1	270	1372
2	674	1133
3	2402	745
4	4507	745
5	4545	745
6	5063	745

prune141.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	134	5	139

Error

0.0b

Counts

139 → 5

Alt Table

Status	Error	Program
	32.8b	(pow.f64 (pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (hypot.f64 1 y))) 2) 3)
▶	0.1b	(.f64 (hypot.f64 1 y) (.f64 (hypot.f64 1 y) x))
✓	4.8b	(fma.f64 x (*.f64 y y) x)
	32.1b	(pow.f64 (*.f64 (sqrt.f64 x) (hypot.f64 1 y)) 2)
	5.0b	(neg.f64 (/.f64 (fma.f64 y y 1) (/.f64 -1 x)))

Compiler

Compiled 2116 to 1455 computations (31.2% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (hypot.f64 1 y) x)
✓	0.1b	(.f64 (hypot.f64 1 y) (.f64 (hypot.f64 1 y) x))

series63.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

36.0ms	(.f64 (hypot.f64 1 y) (.f64 (hypot.f64 1 y) x))
27.0ms	(*.f64 (hypot.f64 1 y) x)

rewrite81.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

541×	`log1p-expm1-u_binary64`
541×	`expm1-log1p-u_binary64`
447×	`unpow-prod-down_binary64`
325×	`log-prod_binary64`
165×	`pow2_binary64`

Counts

2 → 34

Calls

2 calls:

80.0ms	(*.f64 (hypot.f64 1 y) x)
80.0ms	(.f64 (hypot.f64 1 y) (.f64 (hypot.f64 1 y) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	133	17
2	1445	15
3	5446	15
0	0	0
1	0	0

simplify114.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

432×	`distribute-rgt-neg-in_binary64`
343×	`fma-neg_binary64`
335×	`cancel-sign-sub-inv_binary64`
329×	`neg-mul-1_binary64`
291×	`distribute-neg-frac_binary64`

Counts

82 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	49	541
1	146	479
2	391	465
3	1256	461
4	3329	459
5	4505	459
6	4941	459

prune65.0ms (1.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	63	6	69

Error

0.0b

Counts

69 → 6

Alt Table

Status	Error	Program
	5.0b	(neg.f64 (/.f64 (fma.f64 y y 1) (/.f64 -1 x)))
	1.4b	(.f64 (hypot.f64 1 y) (pow.f64 (cbrt.f64 (.f64 (hypot.f64 1 y) x)) 3))
	32.8b	(pow.f64 (pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (hypot.f64 1 y))) 2) 3)
✓	0.1b	(.f64 (hypot.f64 1 y) (.f64 (hypot.f64 1 y) x))
✓	4.8b	(fma.f64 x (*.f64 y y) x)
	32.1b	(pow.f64 (*.f64 (sqrt.f64 x) (hypot.f64 1 y)) 2)

Compiler

Compiled 900 to 609 computations (32.3% saved)

regimes255.0ms (5.1%)

Accuracy

Total 0.1b remaining (75.5%)

Threshold costs 0.1b (75.5%)

Counts

29 → 1

Compiler

Compiled 1937 to 1256 computations (35.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	11	13
2	10	13

end165.0ms (3.3%)

Compiler: Compiled 89 to 66 computations (25.8% saved)

Details

analyze194.0ms (3.9%)

sample1.3s (25.8%)

simplify16.0ms (0.3%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series19.0ms (0.4%)

rewrite92.0ms (1.8%)

simplify182.0ms (3.6%)

prune33.0ms (0.7%)

localize7.0ms (0.1%)

series17.0ms (0.3%)

rewrite109.0ms (2.2%)

simplify170.0ms (3.4%)

prune42.0ms (0.8%)

localize13.0ms (0.3%)

series1.7s (33.4%)

rewrite115.0ms (2.3%)

simplify136.0ms (2.7%)

prune141.0ms (2.8%)

localize10.0ms (0.2%)

series63.0ms (1.2%)

rewrite81.0ms (1.6%)

simplify114.0ms (2.3%)

prune65.0ms (1.3%)

regimes255.0ms (5.1%)

simplify4.0ms (0.1%)

end165.0ms (3.3%)

Profiling