Details

analyze93.0ms (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
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 18 to 8 computations (55.6% saved)

sample781.0ms (34.4%)

Results

752.0ms	8256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 53 to 23 computations (56.6% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
4×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	15	15
2	30	11
3	49	11
4	63	11
5	67	11
6	65	11

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	(fma.f64 y (.f64 y 3) (.f64 x x))
	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

Compiler

Compiled 79 to 36 computations (54.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

series9.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(fma.f64 y (*.f64 y 3) (*.f64 x x))

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 y (*.f64 y 3) (*.f64 x x))

simplify59.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-def_binary64`
466×	`distribute-rgt-in_binary64`
460×	`distribute-lft-in_binary64`
356×	`unswap-sqr_binary64`
323×	`*-commutative_binary64`

Counts

34 → 24

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	394
1	35	371
2	66	371
3	184	371
4	793	371
5	3022	371
6	4320	371
7	5097	371

prune17.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	23	3	26

Error

0.0b

Counts

26 → 3

Alt Table

Status	Error	Program
	40.2b	(cbrt.f64 (pow.f64 (fma.f64 x x (.f64 3 (.f64 y y))) 3))
▶	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 343 to 179 computations (47.8% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 3 (.f64 y y))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(*.f64 3 (*.f64 y y))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 21

Calls

1 calls:

4.0ms

(*.f64 3 (*.f64 y y))

simplify56.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

722×	`fma-def_binary64`
701×	`associate-/l/_binary64`
384×	`distribute-rgt-in_binary64`
347×	`distribute-lft-in_binary64`
212×	`*-commutative_binary64`

Counts

33 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	306
1	76	270
2	175	261
3	419	261
4	633	261
5	1054	261
6	2130	261
7	4875	261
8	4875	261

prune17.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	23	4	27

Error

0.0b

Counts

27 → 4

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
	20.7b	(fma.f64 x x (cbrt.f64 (*.f64 27 (pow.f64 y 6))))
▶	0.3b	(fma.f64 x x (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y y))))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 376 to 216 computations (42.6% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y y)))
✓	0.3b	(.f64 (sqrt.f64 3) (.f64 y y))

series11.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y y)))
4.0ms	(.f64 (sqrt.f64 3) (.f64 y y))

rewrite16.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
12×	`associate-l_binary64`
9×	`cbrt-unprod_binary64`

Counts

2 → 51

Calls

2 calls:

7.0ms	(.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y y)))
6.0ms	(.f64 (sqrt.f64 3) (.f64 y y))

simplify79.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-def_binary64`
580×	`associate-l_binary64`
429×	`*-commutative_binary64`
402×	`associate-r_binary64`
304×	`unswap-sqr_binary64`

Counts

75 → 72

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	62	821
1	136	725
2	392	713
3	1127	699
4	1941	684
5	3158	684
6	4963	684
7	4940	684

prune63.0ms (2.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	69	7	76

Error

0.0b

Counts

76 → 7

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 x x (.f64 (.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3))) (.f64 (cbrt.f64 (sqrt.f64 3)) (.f64 (sqrt.f64 3) (*.f64 y y)))))
✓	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
	20.7b	(fma.f64 x x (cbrt.f64 (*.f64 27 (pow.f64 y 6))))
✓	0.3b	(fma.f64 x x (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y y))))
	0.2b	(fma.f64 x x (.f64 (.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3))) (.f64 (sqrt.f64 3) (.f64 (*.f64 y y) (cbrt.f64 (sqrt.f64 3))))))
	0.2b	(fma.f64 x x (.f64 (sqrt.f64 3) (.f64 (.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3))) (.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 y y)))))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 1415 to 950 computations (32.9% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 (sqrt.f64 3)) (.f64 (sqrt.f64 3) (*.f64 y y)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3))) (.f64 (cbrt.f64 (sqrt.f64 3)) (.f64 (sqrt.f64 3) (*.f64 y y))))
	0.3b	(.f64 (sqrt.f64 3) (.f64 y y))
✓	1.0b	(*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))

series326.0ms (14.3%)

Counts

3 → 24

Calls

3 calls:

318.0ms

(*.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 (sqrt.f64 3) (*.f64 y y)))

8.0ms

(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3))) (*.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 (sqrt.f64 3) (*.f64 y y))))

0.0ms

(*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))

rewrite75.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`pow1_binary64`
46×	`cbrt-prod_binary64`
46×	`add-exp-log_binary64`
40×	`add-sqr-sqrt_binary64`
32×	`pow-prod-down_binary64`

Counts

3 → 123

Calls

3 calls:

47.0ms

(*.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 (sqrt.f64 3) (*.f64 y y)))

13.0ms

(*.f64 (*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3))) (*.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 (sqrt.f64 3) (*.f64 y y))))

7.0ms

(*.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))

simplify164.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

525×	`fma-def_binary64`
414×	`*-commutative_binary64`
376×	`sqr-pow_binary64`
292×	`log-prod_binary64`
279×	`exp-prod_binary64`

Counts

147 → 148

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	2344
1	253	1695
2	875	1558
3	1800	1525
4	3079	1351
5	4812	1351
6	4983	1351
7	4874	1351

prune231.0ms (10.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	2	1	3
Picked	1	0	1
Done	0	3	3
Total	185	5	190

Error

Counts

190 → 5

Alt Table

Status	Error	Program
	0.2b	(fma.f64 x x (.f64 (.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3))) (.f64 (.f64 y y) (cbrt.f64 9))))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
✓	0.3b	(fma.f64 x x (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (*.f64 y y))))
✓	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
	0.2b	(fma.f64 x x (.f64 (sqrt.f64 3) (.f64 (.f64 (cbrt.f64 (sqrt.f64 3)) (cbrt.f64 (sqrt.f64 3))) (.f64 (cbrt.f64 (sqrt.f64 3)) (*.f64 y y)))))

Compiler

Compiled 4904 to 3831 computations (21.9% saved)

regimes124.0ms (5.5%)

Accuracy

Total 0.1b remaining (94.9%)

Threshold costs 0.1b (94.9%)

Counts

23 → 1

Compiler

Compiled 2079 to 1524 computations (26.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11
2	8	11

end106.0ms (4.7%)

Compiler: Compiled 96 to 68 computations (29.2% saved)

Details

analyze93.0ms (4.1%)

sample781.0ms (34.4%)

simplify7.0ms (0.3%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series9.0ms (0.4%)

rewrite1.0ms (0%)

simplify59.0ms (2.6%)

prune17.0ms (0.7%)

localize5.0ms (0.2%)

series3.0ms (0.1%)

rewrite5.0ms (0.2%)

simplify56.0ms (2.4%)

prune17.0ms (0.8%)

localize6.0ms (0.3%)

series11.0ms (0.5%)

rewrite16.0ms (0.7%)

simplify79.0ms (3.5%)

prune63.0ms (2.8%)

localize11.0ms (0.5%)

series326.0ms (14.3%)

rewrite75.0ms (3.3%)

simplify164.0ms (7.2%)

prune231.0ms (10.2%)

regimes124.0ms (5.5%)

simplify2.0ms (0.1%)

end106.0ms (4.7%)

Profiling