Details

analyze464.0ms (14.9%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
37.4%	62.4%	0.1%	8
40.6%	56.9%	2.5%	9
45.2%	50.7%	4%	10
57.7%	33.5%	8.7%	11
59.7%	29.4%	11%	12
62%	25%	13%	13
68.3%	17.4%	14.4%	14

Compiler

Compiled 17 to 12 computations (29.4% saved)

sample1.1s (34.3%)

Symmetry

(sort d2 d3)

Results

930.0ms	8217×	body	128	valid
87.0ms	665×	body	128	invalid
6.0ms	17×	body	1024	valid
4.0ms	16×	body	512	valid
1.0ms	6×	body	256	valid

Compiler

Compiled 50 to 35 computations (30% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

114×	`fma-def_binary64`
61×	`associate-+l+_binary64`
40×	`associate-+r+_binary64`
34×	`distribute-lft-out_binary64`
33×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	21	14
2	50	10
3	125	10
4	216	10
5	237	10
6	249	10
7	235	10

prune3.0ms (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
	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
▶	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))

Compiler

Compiled 75 to 51 computations (32% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))

series8.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

8.0ms

(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
5×	`associate-r_binary64`
5×	`add-sqr-sqrt_binary64`
3×	`distribute-lft-out_binary64`
3×	`associate-l_binary64`

Counts

1 → 26

Calls

1 calls:

6.0ms

(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))

simplify61.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

961×	`distribute-rgt-in_binary64`
953×	`distribute-lft-in_binary64`
416×	`associate-l_binary64`
318×	`associate-r_binary64`
261×	`fma-def_binary64`

Counts

62 → 50

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	687
1	163	645
2	700	643
3	4006	643
4	4316	643
5	5142	643

prune33.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	48	2	50
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	48	4	52

Error

Counts

52 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
	28.6b	(/.f64 (.f64 d1 (fma.f64 (+.f64 37 d3) (-.f64 -37 d3) (.f64 d2 d2))) (-.f64 d2 (+.f64 d3 37)))
▶	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
	22.6b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37)))) (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))

Compiler

Compiled 752 to 449 computations (40.3% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1))
✓	0.0b	(*.f64 (+.f64 d3 5) d1)
✓	0.0b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))

series25.0ms (0.8%)

Counts

3 → 96

Calls

3 calls:

12.0ms	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
9.0ms	(+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1))
4.0ms	(*.f64 (+.f64 d3 5) d1)

rewrite200.0ms (6.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 55

Calls

3 calls:

190.0ms	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
4.0ms	(*.f64 (+.f64 d3 5) d1)
3.0ms	(+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1))

simplify127.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

810×	`fma-def_binary64`
695×	`fma-neg_binary64`
486×	`cancel-sign-sub-inv_binary64`
332×	`*-commutative_binary64`
298×	`associate-+l+_binary64`

Counts

151 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	121	1635
1	348	1544
2	1326	1485
3	3601	1483
4	4941	1483
5	4843	1483

prune100.0ms (3.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	108	4	112

Error

Counts

112 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
	28.6b	(/.f64 (.f64 d1 (fma.f64 (+.f64 37 d3) (-.f64 -37 d3) (.f64 d2 d2))) (-.f64 d2 (+.f64 d3 37)))
✓	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
▶	22.6b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37)))) (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))

Compiler

Compiled 2046 to 1217 computations (40.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 d2 (+.f64 d3 37)))
✓	0.2b	(*.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))
✓	0.2b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37)))) (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))

series88.0ms (2.8%)

Counts

3 → 64

Calls

3 calls:

51.0ms	(*.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))
29.0ms	(sqrt.f64 (+.f64 d2 (+.f64 d3 37)))
8.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37)))) (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))

rewrite58.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
16×	`sqrt-prod_binary64`
16×	`associate-r_binary64`
16×	`sqrt-div_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

3 → 81

Calls

3 calls:

40.0ms	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37)))) (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))
7.0ms	(*.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))
5.0ms	(sqrt.f64 (+.f64 d2 (+.f64 d3 37)))

simplify88.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

699×	`distribute-rgt-in_binary64`
680×	`distribute-lft-in_binary64`
605×	`fma-def_binary64`
243×	`associate-l_binary64`
192×	`associate-r_binary64`

Counts

145 → 156

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	196	2557
1	501	2401
2	1562	2345
3	4909	2343
4	4973	2343

prune120.0ms (3.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	199	4	203

Error

Counts

203 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
▶	28.6b	(/.f64 (.f64 d1 (fma.f64 (+.f64 37 d3) (-.f64 -37 d3) (.f64 d2 d2))) (-.f64 d2 (+.f64 d3 37)))
✓	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
✓	22.6b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37)))) (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))

Compiler

Compiled 5067 to 3496 computations (31% saved)

localize12.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	1.5b	(fma.f64 (+.f64 37 d3) (-.f64 -37 d3) (*.f64 d2 d2))
✓	9.6b	(.f64 d1 (fma.f64 (+.f64 37 d3) (-.f64 -37 d3) (.f64 d2 d2)))
✓	17.3b	(/.f64 (.f64 d1 (fma.f64 (+.f64 37 d3) (-.f64 -37 d3) (.f64 d2 d2))) (-.f64 d2 (+.f64 d3 37)))

series100.0ms (3.2%)

Counts

3 → 96

Calls

3 calls:

60.0ms

(/.f64 (*.f64 d1 (fma.f64 (+.f64 37 d3) (-.f64 -37 d3) (*.f64 d2 d2))) (-.f64 d2 (+.f64 d3 37)))

32.0ms

(*.f64 d1 (fma.f64 (+.f64 37 d3) (-.f64 -37 d3) (*.f64 d2 d2)))

8.0ms

(fma.f64 (+.f64 37 d3) (-.f64 -37 d3) (*.f64 d2 d2))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 63

Calls

3 calls:

6.0ms

(/.f64 (*.f64 d1 (fma.f64 (+.f64 37 d3) (-.f64 -37 d3) (*.f64 d2 d2))) (-.f64 d2 (+.f64 d3 37)))

4.0ms

(*.f64 d1 (fma.f64 (+.f64 37 d3) (-.f64 -37 d3) (*.f64 d2 d2)))

0.0ms

(fma.f64 (+.f64 37 d3) (-.f64 -37 d3) (*.f64 d2 d2))

simplify113.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

419×	`fma-neg_binary64`
248×	`associate-/l*_binary64`
220×	`cancel-sign-sub-inv_binary64`
202×	`times-frac_binary64`
179×	`sub-neg_binary64`

Counts

159 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	251	4238
1	738	3715
2	3214	3593
3	4620	3589
4	4967	3589

prune107.0ms (3.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	154	4	158

Error

Counts

158 → 4

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 d1 (+.f64 d2 (+.f64 d3 37)))
✓	28.6b	(/.f64 (.f64 d1 (fma.f64 (+.f64 37 d3) (-.f64 -37 d3) (.f64 d2 d2))) (-.f64 d2 (+.f64 d3 37)))
✓	0.1b	(+.f64 (+.f64 (.f64 d1 d2) (.f64 (+.f64 d3 5) d1)) (*.f64 d1 32))
✓	22.6b	(.f64 (.f64 d1 (sqrt.f64 (+.f64 d2 (+.f64 d3 37)))) (sqrt.f64 (+.f64 d2 (+.f64 d3 37))))

Compiler

Compiled 4615 to 2849 computations (38.3% saved)

regimes226.0ms (7.2%)

Accuracy

Total 0.0b remaining (77.5%)

Threshold costs 0.0b (77.5%)

Counts

51 → 1

Compiler

Compiled 3894 to 2755 computations (29.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	11	10
2	11	10

end66.0ms (2.1%)

Remove: (sort d2 d3)
Compiler: Compiled 105 to 73 computations (30.5% saved)

Details

analyze464.0ms (14.9%)

sample1.1s (34.3%)

simplify9.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite7.0ms (0.2%)

simplify61.0ms (1.9%)

prune33.0ms (1.1%)

localize8.0ms (0.3%)

series25.0ms (0.8%)

rewrite200.0ms (6.4%)

simplify127.0ms (4.1%)

prune100.0ms (3.2%)

localize7.0ms (0.2%)

series88.0ms (2.8%)

rewrite58.0ms (1.8%)

simplify88.0ms (2.8%)

prune120.0ms (3.8%)

localize12.0ms (0.4%)

series100.0ms (3.2%)

rewrite14.0ms (0.4%)

simplify113.0ms (3.6%)

prune107.0ms (3.4%)

regimes226.0ms (7.2%)

simplify2.0ms (0.1%)

end66.0ms (2.1%)

Profiling