Details

analyze103.0ms (2.9%)

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
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 (30.1%)

Results

998.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify42.0ms (1.2%)

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

Compiler

Compiled 97 to 64 computations (34% saved)

localize7.0ms (0.2%)

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)

series66.0ms (1.9%)

Counts

3 → 72

Calls

3 calls:

30.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
27.0ms	(pow.f64 (hypot.f64 a b) 4)
9.0ms	(hypot.f64 a b)

rewrite8.0ms (0.2%)

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)

simplify104.0ms (2.9%)

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

prune124.0ms (3.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	111	4	115

Error

Counts

115 → 4

Alt Table

Status	Error	Program
	0.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
▶	0.0b	(-.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))) 1)
	0.4b	(.f64 (.f64 (cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (.f64 b 4) -1))) (cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (.f64 b 4) -1)))) (cbrt.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))))
	14.8b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3))

Compiler

Compiled 2469 to 1595 computations (35.4% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))
✓	0.0b	(+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4))
✓	0.0b	(*.f64 4 (pow.f64 b 2))
✓	2.4b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series31.0ms (0.9%)

Counts

4 → 3

Calls

4 calls:

15.0ms	(.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))
10.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
3.0ms	(+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4))
2.0ms	(*.f64 4 (pow.f64 b 2))

rewrite27.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-exp-log_binary64`
34×	`add-sqr-sqrt_binary64`
31×	`prod-exp_binary64`
20×	`unswap-sqr_binary64`
18×	`unpow-prod-down_binary64`

Counts

4 → 123

Calls

4 calls:

6.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
5.0ms	(.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2)))
5.0ms	(+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4))
4.0ms	(*.f64 4 (pow.f64 b 2))

simplify95.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

404×	`fma-neg_binary64`
362×	`*-commutative_binary64`
286×	`sqr-pow_binary64`
233×	`associate-+l+_binary64`
217×	`associate-+r+_binary64`

Counts

126 → 172

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	162	1538
1	321	1343
2	936	1318
3	1992	1244
4	3895	1234
5	4909	1234
6	4945	1234

prune305.0ms (8.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	172	4	176

Error

Counts

176 → 4

Alt Table

Status	Error	Program
	7.3b	(-.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (cbrt.f64 (*.f64 (pow.f64 b 6) (pow.f64 (fma.f64 b b 4) 3))))) 1)
▶	0.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(-.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))) 1)
	14.8b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3))

Compiler

Compiled 5471 to 4154 computations (24.1% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 a a) (.f64 b b))
✓	0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

series37.0ms (1.1%)

Counts

3 → 72

Calls

3 calls:

19.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
12.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
6.0ms	(+.f64 (.f64 a a) (.f64 b b))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`fma-def_binary64`
9×	`*-un-lft-identity_binary64`
7×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 57

Calls

3 calls:

9.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
3.0ms	(+.f64 (.f64 a a) (.f64 b b))

simplify121.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-def_binary64`
541×	`fma-neg_binary64`
450×	`associate-l_binary64`
400×	`associate-r_binary64`
310×	`distribute-rgt-in_binary64`

Counts

129 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	2036
1	286	1858
2	879	1687
3	4101	1685
4	4964	1685
5	4990	1685
6	4935	1685

prune111.0ms (3.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	113	4	117

Error

Counts

117 → 4

Alt Table

Status	Error	Program
▶	7.3b	(-.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (cbrt.f64 (*.f64 (pow.f64 b 6) (pow.f64 (fma.f64 b b 4) 3))))) 1)
✓	0.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(-.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))) 1)
	14.8b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3))

Compiler

Compiled 2582 to 1402 computations (45.7% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (pow.f64 b 6) (pow.f64 (fma.f64 b b 4) 3))
✓	0.1b	(pow.f64 (fma.f64 b b 4) 3)
	2.4b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
✓	20.4b	(cbrt.f64 (*.f64 (pow.f64 b 6) (pow.f64 (fma.f64 b b 4) 3)))

series10.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(*.f64 (pow.f64 b 6) (pow.f64 (fma.f64 b b 4) 3))
3.0ms	(cbrt.f64 (*.f64 (pow.f64 b 6) (pow.f64 (fma.f64 b b 4) 3)))
3.0ms	(pow.f64 (fma.f64 b b 4) 3)

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
16×	`unpow-prod-down_binary64`
16×	`add-exp-log_binary64`
12×	`associate-r_binary64`
12×	`unswap-sqr_binary64`

Counts

3 → 87

Calls

3 calls:

6.0ms	(*.f64 (pow.f64 b 6) (pow.f64 (fma.f64 b b 4) 3))
3.0ms	(cbrt.f64 (*.f64 (pow.f64 b 6) (pow.f64 (fma.f64 b b 4) 3)))
2.0ms	(pow.f64 (fma.f64 b b 4) 3)

simplify92.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

858×	`fma-def_binary64`
698×	`exp-prod_binary64`
630×	`unswap-sqr_binary64`
561×	`log-prod_binary64`
396×	`*-commutative_binary64`

Counts

123 → 124

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	127	1940
1	262	1855
2	1020	1819
3	2590	1759
4	4413	1741
5	5283	1741

prune292.0ms (8.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	194	4	198

Error

Counts

198 → 4

Alt Table

Status	Error	Program
✓	7.3b	(-.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (cbrt.f64 (*.f64 (pow.f64 b 6) (pow.f64 (fma.f64 b b 4) 3))))) 1)
✓	0.2b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(-.f64 (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (*.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))) 1)
	14.8b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)) 3))

Compiler

Compiled 6522 to 4966 computations (23.9% saved)

regimes701.0ms (19.8%)

Accuracy

Total 0.0b remaining (59.2%)

Threshold costs 0.0b (59.2%)

Counts

113 → 1

Compiler

Compiled 13392 to 9855 computations (26.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	26	35
2	27	35
3	25	35

end111.0ms (3.1%)

Compiler: Compiled 143 to 110 computations (23.1% saved)

Details

analyze103.0ms (2.9%)

sample1.1s (30.1%)

simplify42.0ms (1.2%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series66.0ms (1.9%)

rewrite8.0ms (0.2%)

simplify104.0ms (2.9%)

prune124.0ms (3.5%)

localize14.0ms (0.4%)

series31.0ms (0.9%)

rewrite27.0ms (0.8%)

simplify95.0ms (2.7%)

prune305.0ms (8.6%)

localize9.0ms (0.3%)

series37.0ms (1.1%)

rewrite18.0ms (0.5%)

simplify121.0ms (3.4%)

prune111.0ms (3.1%)

localize17.0ms (0.5%)

series10.0ms (0.3%)

rewrite16.0ms (0.5%)

simplify92.0ms (2.6%)

prune292.0ms (8.3%)

regimes701.0ms (19.8%)

simplify2.0ms (0.1%)

end111.0ms (3.1%)

Profiling