Details

analyze107.0ms (3.6%)

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)

sample1.1s (35.9%)

Results

1.0s	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify47.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

770×	`unswap-sqr_binary64`
631×	`associate-l_binary64`
623×	`fma-def_binary64`
311×	`fma-neg_binary64`
283×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	30	21
2	60	21
3	159	21
4	518	17
5	1687	17
6	3597	17
7	5026	17

prune4.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 97 to 64 computations (34% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a b)
✓	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)

series89.0ms (3%)

Counts

3 → 72

Calls

3 calls:

42.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
35.0ms	(pow.f64 (hypot.f64 a b) 4)
12.0ms	(hypot.f64 a b)

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
7×	`fma-def_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`unpow-prod-down_binary64`

Counts

3 → 52

Calls

3 calls:

4.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
1.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(hypot.f64 a b)

simplify102.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-neg_binary64`
421×	`fma-def_binary64`
280×	`associate-r_binary64`
276×	`associate-l_binary64`
184×	`times-frac_binary64`

Counts

124 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	2123
1	343	2010
2	979	1901
3	4070	1899
4	4922	1899
5	4944	1899

prune108.0ms (3.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	2	115

Error

Counts

115 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (pow.f64 a 4) (+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) -1))
	16.6b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3))

Compiler

Compiled 2335 to 1499 computations (35.8% saved)

localize11.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.2b	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

series30.0ms (1%)

Counts

1 → 24

Calls

1 calls:

30.0ms

(fma.f64 (*.f64 b b) (fma.f64 2 (*.f64 a a) 4) (pow.f64 b 4))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (*.f64 b b) (fma.f64 2 (*.f64 a a) 4) (pow.f64 b 4))

simplify55.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

836×	`associate-l_binary64`
694×	`associate-r_binary64`
472×	`unswap-sqr_binary64`
415×	`exp-prod_binary64`
398×	`distribute-rgt-in_binary64`

Counts

34 → 27

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	745
1	54	600
2	139	600
3	542	600
4	3349	600
5	5042	600

prune28.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	27	2	29

Error

Counts

29 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 a 4) (+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) -1))
▶	16.6b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3))

Compiler

Compiled 692 to 437 computations (36.8% saved)

localize11.0ms (0.4%)

Local error

Found 4 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)
✓	0.1b	(pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3)
✓	15.5b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3))

series111.0ms (3.7%)

Counts

2 → 48

Calls

2 calls:

69.0ms	(pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3)
41.0ms	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
14×	`cbrt-prod_binary64`
8×	`cube-prod_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`unpow-prod-down_binary64`

Counts

2 → 56

Calls

2 calls:

5.0ms	(pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3)
4.0ms	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3))

simplify117.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

425×	`fma-def_binary64`
419×	`associate-+r+_binary64`
369×	`unswap-sqr_binary64`
271×	`associate-+l+_binary64`
248×	`+-commutative_binary64`

Counts

104 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	3925
1	840	3624
2	3394	3606
3	4715	3606
4	4950	3606

prune182.0ms (6.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	185	2	187

Error

Counts

187 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 a 4) (+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) -1))
✓	16.6b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3))

Compiler

Compiled 5619 to 3901 computations (30.6% saved)

regimes816.0ms (27.2%)

Accuracy

Total 0.0b remaining (17%)

Threshold costs 0.0b (17%)

Counts

119 → 1

Compiler

Compiled 12553 to 9422 computations (24.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	16	27
2	16	27

end69.0ms (2.3%)

Compiler: Compiled 80 to 58 computations (27.5% saved)

Details

analyze107.0ms (3.6%)

sample1.1s (35.9%)

simplify47.0ms (1.6%)

prune4.0ms (0.1%)

localize8.0ms (0.3%)

series89.0ms (3%)

rewrite8.0ms (0.3%)

simplify102.0ms (3.4%)

prune108.0ms (3.6%)

localize11.0ms (0.4%)

series30.0ms (1%)

rewrite1.0ms (0%)

simplify55.0ms (1.8%)

prune28.0ms (1%)

localize11.0ms (0.4%)

series111.0ms (3.7%)

rewrite14.0ms (0.5%)

simplify117.0ms (3.9%)

prune182.0ms (6.1%)

regimes816.0ms (27.2%)

simplify3.0ms (0.1%)

end69.0ms (2.3%)

Profiling