Details

analyze122.0ms (3.7%)

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)

sample800.0ms (24.7%)

Results

753.0ms	8256×	body	128	valid
16.0ms	202×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify9.0ms (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

prune2.0ms (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

6.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.1b	(*.f64 x (fma.f64 y y 1))

Compiler

Compiled 31 to 19 computations (38.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.6b	(*.f64 x (fma.f64 y y 1))

series9.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

9.0ms

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

rewrite92.0ms (2.8%)

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 → 22

Calls

1 calls:

92.0ms

(*.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

simplify146.0ms (4.5%)

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

46 → 28

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

prune19.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	24	4	28
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	4	29

Error

3.5b

Counts

29 → 4

Alt Table

Status	Error	Program
	32.0b	(pow.f64 (*.f64 (sqrt.f64 x) (hypot.f64 1 y)) 2)
	7.3b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 y y 1))) 3)
▶	6.1b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	24.2b	x

Compiler

Compiled 304 to 188 computations (38.2% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	9.8b	(*.f64 (pow.f64 y 2) x)

series15.0ms (0.5%)

Counts

1 → 0

Calls

1 calls:

15.0ms

(*.f64 (pow.f64 y 2) x)

rewrite75.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

865×	`log1p-udef_binary64`
461×	`log1p-expm1-u_binary64`
461×	`expm1-log1p-u_binary64`
319×	`unpow-prod-down_binary64`
254×	`log-prod_binary64`

Counts

1 → 18

Calls

1 calls:

74.0ms

(*.f64 (pow.f64 y 2) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1230	7
3	4870	7
4	6293	7
0	0	0
1	0	0

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune16.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	17	5	22

Error

3.5b

Counts

22 → 5

Alt Table

Status	Error	Program
	32.0b	(pow.f64 (*.f64 (sqrt.f64 x) (hypot.f64 1 y)) 2)
▶	7.3b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 y y 1))) 3)
	38.9b	(+.f64 (sqrt.f64 (pow.f64 (*.f64 y (sqrt.f64 x)) 4)) x)
✓	6.1b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	24.2b	x

Compiler

Compiled 271 to 133 computations (50.9% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (*.f64 x (fma.f64 y y 1)))
✓	0.6b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 y y 1))) 3)
	5.6b	(*.f64 x (fma.f64 y y 1))

series921.0ms (28.4%)

Counts

2 → 48

Calls

2 calls:

549.0ms	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 y y 1))) 3)
372.0ms	(cbrt.f64 (*.f64 x (fma.f64 y y 1)))

rewrite73.0ms (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 → 68

Calls

2 calls:

72.0ms	(cbrt.f64 (*.f64 x (fma.f64 y y 1)))
72.0ms	(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

simplify91.0ms (2.8%)

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

116 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	1450
1	270	1372
2	674	1171
3	2402	745
4	4507	745
5	4545	745
6	5063	745

prune85.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	128	4	132
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	131	6	137

Error

0.0b

Counts

137 → 6

Alt Table

Status	Error	Program
	6.4b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (fma.f64 y y 1)) 2)) (cbrt.f64 (fma.f64 y y 1)))
▶	0.2b	(.f64 (hypot.f64 1 y) (.f64 (hypot.f64 1 y) x))
	7.2b	(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (fma.f64 y y 1)) (pow.f64 (cbrt.f64 (*.f64 x (fma.f64 y y 1))) 2)))
	32.0b	(pow.f64 (*.f64 (sqrt.f64 x) (hypot.f64 1 y)) 2)
✓	6.1b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	32.5b	(pow.f64 (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 x) (hypot.f64 1 y)) 2)) 3)

Compiler

Compiled 2194 to 1515 computations (30.9% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series37.0ms (1.1%)

Counts

3 → 60

Calls

3 calls:

20.0ms	(.f64 (hypot.f64 1 y) (.f64 (hypot.f64 1 y) x))
14.0ms	(*.f64 (hypot.f64 1 y) x)
2.0ms	(hypot.f64 1 y)

rewrite46.0ms (1.4%)

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

3 → 71

Calls

3 calls:

44.0ms	(hypot.f64 1 y)
44.0ms	(*.f64 (hypot.f64 1 y) x)
44.0ms	(.f64 (hypot.f64 1 y) (.f64 (hypot.f64 1 y) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	24
1	133	21
2	1445	19
3	5446	19
0	0	0
1	0	0

simplify81.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

468×	`fma-neg_binary64`
445×	`cancel-sign-sub-inv_binary64`
292×	`sub-neg_binary64`
272×	`fma-def_binary64`
271×	`times-frac_binary64`

Counts

131 → 123

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	699
1	224	630
2	596	609
3	1811	597
4	4292	597
5	4815	597
6	5050	597

prune140.0ms (4.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	175	5	180
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	177	9	186

Error

0.0b

Counts

186 → 9

Alt Table

Status	Error	Program
	6.4b	(.f64 (.f64 x (pow.f64 (cbrt.f64 (fma.f64 y y 1)) 2)) (cbrt.f64 (fma.f64 y y 1)))
✓	0.2b	(.f64 (hypot.f64 1 y) (.f64 (hypot.f64 1 y) x))
	11.4b	(.f64 (cbrt.f64 (pow.f64 (hypot.f64 1 y) 3)) (.f64 (hypot.f64 1 y) x))
	0.3b	(.f64 (pow.f64 (sqrt.f64 (hypot.f64 1 y)) 2) (.f64 (hypot.f64 1 y) x))
	0.5b	(.f64 (pow.f64 (cbrt.f64 (hypot.f64 1 y)) 3) (.f64 (hypot.f64 1 y) x))
	0.7b	(.f64 (.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 1 y))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 1 y))) 3)) (*.f64 (hypot.f64 1 y) x))
✓	6.1b	(+.f64 (*.f64 (pow.f64 y 2) x) x)
	1.4b	(.f64 (hypot.f64 1 y) (pow.f64 (cbrt.f64 (.f64 (hypot.f64 1 y) x)) 3))
	32.5b	(pow.f64 (cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 x) (hypot.f64 1 y)) 2)) 3)

Compiler

Compiled 2793 to 2005 computations (28.2% saved)

regimes296.0ms (9.1%)

Accuracy

Total 0.1b remaining (79.8%)

Threshold costs 0.1b (79.8%)

Counts

64 → 1

Compiler

Compiled 4070 to 2968 computations (27.1% saved)

simplify2.0ms (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

end143.0ms (4.4%)

Compiler: Compiled 151 to 116 computations (23.2% saved)

Details

analyze122.0ms (3.7%)

sample800.0ms (24.7%)

simplify9.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.3%)

rewrite92.0ms (2.8%)

simplify146.0ms (4.5%)

prune19.0ms (0.6%)

localize4.0ms (0.1%)

series15.0ms (0.5%)

rewrite75.0ms (2.3%)

simplify6.0ms (0.2%)

prune16.0ms (0.5%)

localize6.0ms (0.2%)

series921.0ms (28.4%)

rewrite73.0ms (2.3%)

simplify91.0ms (2.8%)

prune85.0ms (2.6%)

localize5.0ms (0.1%)

series37.0ms (1.1%)

rewrite46.0ms (1.4%)

simplify81.0ms (2.5%)

prune140.0ms (4.3%)

regimes296.0ms (9.1%)

simplify2.0ms (0.1%)

end143.0ms (4.4%)

Profiling