Details

analyze95.0ms (4.1%)

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
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample916.0ms (39.4%)

Results

900.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 40 to 26 computations (35% saved)

preprocess29.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

931×	`fma-def_binary64`
495×	`fma-neg_binary64`
420×	`associate-+l+_binary64`
334×	`associate-+r+_binary64`
241×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	46
1	48	42
2	99	42
3	288	42
4	1136	34
5	3734	34
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 19 to 12 computations (36.8% saved)

simplify23.0ms (1%)

Algorithm

1×	egg-herbie

Rules

612×	`fma-def_binary64`
603×	`associate-l_binary64`
311×	`fma-neg_binary64`
233×	`associate-+l+_binary64`
216×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	30	21
2	64	21
3	193	21
4	779	17
5	2634	17

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 59 to 40 computations (32.2% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)

series58.0ms (2.5%)

Counts

2 → 48

Calls

12 calls:

9.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))	b	inf
7.0ms	(pow.f64 (hypot.f64 a b) 4)	a	-inf
5.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))	b	-inf
5.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))	a	-inf
5.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))	a	inf

rewrite50.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

626×	`prod-diff_binary64`
243×	`fma-def_binary64`
181×	`expm1-udef_binary64`
181×	`log1p-udef_binary64`
159×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	212	24
2	2603	24

Stop Event

1×	node limit

Counts

2 → 74

simplify43.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

922×	`fma-def_binary64`
730×	`fma-neg_binary64`
348×	`unswap-sqr_binary64`
321×	`associate-l_binary64`
306×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	26	983
1	72	939
2	211	849
3	811	823
4	2915	823

Stop Event

1×	node limit

Counts

122 → 94

prune105.0ms (4.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	2	95

Error

Counts

95 → 2

Alt Table

Status	Error	Program
	0.1b	(+.f64 (pow.f64 a 4) (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) (fma.f64 b b 4)) -1))
▶	0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))

Status

Error

Program

0.1b

(+.f64 (pow.f64 a 4) (fma.f64 (*.f64 b b) (fma.f64 2 (*.f64 a a) (fma.f64 b b 4)) -1))

▶

0.0b

(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 1872 to 1211 computations (35.3% saved)

localize13.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))
✓	3.0b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series46.0ms (2%)

Counts

3 → 24

Calls

18 calls:

7.0ms	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))	b	0
4.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))	a	-inf
3.0ms	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))	a	0
3.0ms	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))	a	inf
3.0ms	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))	a	-inf

rewrite43.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

178×	`log1p-expm1-u_binary64`
178×	`expm1-log1p-u_binary64`
176×	`add-sqr-sqrt_binary64`
174×	`add-cbrt-cube_binary64`
168×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	47
1	382	47

Stop Event

1×	node limit

Counts

3 → 68

simplify31.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

924×	`fma-def_binary64`
720×	`fma-neg_binary64`
348×	`unswap-sqr_binary64`
328×	`associate-l_binary64`
306×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	575
1	66	537
2	196	471
3	782	445
4	2943	445

Stop Event

1×	node limit

Counts

92 → 84

prune85.0ms (3.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	84	2	86

Error

Counts

86 → 2

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (pow.f64 a 4) (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) (fma.f64 b b 4)) -1))
✓	0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))

Status

Error

Program

▶

0.1b

(+.f64 (pow.f64 a 4) (fma.f64 (*.f64 b b) (fma.f64 2 (*.f64 a a) (fma.f64 b b 4)) -1))

✓

0.0b

(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 2530 to 1769 computations (30.1% saved)

localize10.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) (fma.f64 b b 4)) -1)

series16.0ms (0.7%)

Counts

1 → 24

Calls

6 calls:

5.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) (fma.f64 b b 4)) -1)	a	inf
3.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) (fma.f64 b b 4)) -1)	a	-inf
3.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) (fma.f64 b b 4)) -1)	a	0
2.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) (fma.f64 b b 4)) -1)	b	-inf
2.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) (fma.f64 b b 4)) -1)	b	inf

rewrite36.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

823×	`log1p-expm1-u_binary64`
823×	`expm1-log1p-u_binary64`
98×	`add-sqr-sqrt_binary64`
94×	`add-cbrt-cube_binary64`
94×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	213	19
2	2295	19

Stop Event

1×	node limit

Counts

1 → 23

simplify27.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

904×	`fma-def_binary64`
371×	`fma-neg_binary64`
317×	`*-commutative_binary64`
300×	`unswap-sqr_binary64`
288×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	525
1	51	487
2	142	413
3	491	383
4	1832	383

Stop Event

1×	node limit

Counts

47 → 35

prune36.0ms (1.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	35	2	37

Error

Counts

37 → 2

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (pow.f64 a 4) (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) (fma.f64 b b 4)) -1))
✓	0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))

Status

Error

Program

✓

0.1b

(+.f64 (pow.f64 a 4) (fma.f64 (*.f64 b b) (fma.f64 2 (*.f64 a a) (fma.f64 b b 4)) -1))

✓

0.0b

(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2))) (pow.f64 b 4))) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 829 to 502 computations (39.4% saved)

regimes575.0ms (24.7%)

Accuracy

Total 0.0b remaining (50%)

Threshold costs 0.0b (50%)

Counts

99 → 1

Compiler

Compiled 11161 to 8073 computations (27.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	31
1	21	31

Stop Event

1×

saturated

end75.0ms (3.2%)

Stop Event

1×

done

Compiler

Compiled 94 to 69 computations (26.6% saved)

Details

analyze95.0ms (4.1%)

sample916.0ms (39.4%)

preprocess29.0ms (1.2%)

simplify23.0ms (1%)

prune3.0ms (0.1%)

localize7.0ms (0.3%)

series58.0ms (2.5%)

rewrite50.0ms (2.2%)

simplify43.0ms (1.8%)

prune105.0ms (4.5%)

localize13.0ms (0.6%)

series46.0ms (2%)

rewrite43.0ms (1.8%)

simplify31.0ms (1.3%)

prune85.0ms (3.7%)

localize10.0ms (0.4%)

series16.0ms (0.7%)

rewrite36.0ms (1.5%)

simplify27.0ms (1.2%)

prune36.0ms (1.6%)

regimes575.0ms (24.7%)

simplify2.0ms (0.1%)

end75.0ms (3.2%)

Profiling