Details

analyze175.0ms (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
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample1.3s (28.2%)

Results

1.2s	8256×	body	128	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
340×	`+-commutative_binary64`
277×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	170	36
3	542	36
4	1867	32
5	3281	32
6	4881	32
7	4958	32

prune5.0ms (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 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
▶	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Status

Error

Program

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)

▶

0.0b

(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 172 to 108 computations (37.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a -3 1)
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
✓	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.8b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series58.0ms (1.3%)

Counts

4 → 84

Calls

4 calls:

34.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
13.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
9.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
2.0ms	(fma.f64 a -3 1)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`fma-udef_binary64`

Counts

4 → 53

Calls

4 calls:

4.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
0.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
0.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
0.0ms	(fma.f64 a -3 1)

simplify102.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
528×	`fma-neg_binary64`
415×	`associate-+l+_binary64`
313×	`cancel-sign-sub-inv_binary64`
229×	`associate-+r+_binary64`

Counts

137 → 125

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	2754
1	318	2352
2	969	2192
3	3184	2169
4	4818	2143
5	4983	2143

prune144.0ms (3.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	123	4	127

Error

0.0b

Counts

127 → 4

Alt Table

Status	Error	Program
	14.1b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 a)) -1)
▶	0.2b	(+.f64 (.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
	17.1b	(+.f64 (cbrt.f64 (.f64 (.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 3720 to 2069 computations (44.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.2b	(.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))))
	0.8b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	8.6b	(sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))

series108.0ms (2.4%)

Counts

2 → 48

Calls

2 calls:

75.0ms

(sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))

33.0ms

(*.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 68

Calls

2 calls:

7.0ms

(*.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))))

1.0ms

(sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))

simplify140.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

757×	`times-frac_binary64`
457×	`cancel-sign-sub-inv_binary64`
333×	`fma-def_binary64`
265×	`associate-r_binary64`
256×	`associate-+r+_binary64`

Counts

116 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	289	5926
1	859	5283
2	3236	4999
3	4570	4940
4	5651	4940

prune637.0ms (14.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	311	1	312
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	313	3	316

Error

0.0b

Counts

316 → 3

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
▶	7.5b	(+.f64 (.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) 3))) -1)

Compiler

Compiled 19824 to 11384 computations (42.6% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) 3)))
	0.8b	(.f64 (.f64 b b) (fma.f64 a -3 1))
	8.6b	(sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))
✓	23.3b	(cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) 3))

series123.0ms (2.7%)

Counts

2 → 48

Calls

2 calls:

69.0ms

(cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) 3))

54.0ms

(*.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) 3)))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`cbrt-prod_binary64`
41×	`add-sqr-sqrt_binary64`
26×	`sqrt-prod_binary64`
21×	`associate-r_binary64`
16×	`cube-prod_binary64`

Counts

2 → 83

Calls

2 calls:

9.0ms

(*.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) 3)))

2.0ms

(cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) 3))

simplify205.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

457×	`cancel-sign-sub-inv_binary64`
333×	`fma-def_binary64`
298×	`associate-r_binary64`
292×	`unswap-sqr_binary64`
256×	`associate-+r+_binary64`

Counts

131 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	318	7536
1	898	6913
2	3434	6683
3	4820	6669
4	4989	6669
5	4957	6669

prune595.0ms (13.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	320	0	320
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	320	3	323

Error

0.0b

Counts

323 → 3

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	7.5b	(+.f64 (.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (sqrt.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) 3))) -1)

Compiler

Compiled 23783 to 14397 computations (39.5% saved)

regimes661.0ms (14.8%)

Accuracy

Total 0.1b remaining (76.2%)

Threshold costs 0.1b (76.2%)

Counts

110 → 1

Compiler

Compiled 19179 to 12573 computations (34.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	13	25
2	13	25

end101.0ms (2.3%)

Compiler: Compiled 166 to 99 computations (40.4% saved)

Details

analyze175.0ms (3.9%)

sample1.3s (28.2%)

simplify63.0ms (1.4%)

prune5.0ms (0.1%)

localize13.0ms (0.3%)

series58.0ms (1.3%)

rewrite7.0ms (0.2%)

simplify102.0ms (2.3%)

prune144.0ms (3.2%)

localize15.0ms (0.3%)

series108.0ms (2.4%)

rewrite16.0ms (0.4%)

simplify140.0ms (3.1%)

prune637.0ms (14.2%)

localize22.0ms (0.5%)

series123.0ms (2.7%)

rewrite27.0ms (0.6%)

simplify205.0ms (4.6%)

prune595.0ms (13.3%)

regimes661.0ms (14.8%)

simplify2.0ms (0%)

end101.0ms (2.3%)

Profiling