Details

analyze7.0ms (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample86.0ms (4.7%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 30 to 24 computations (20% saved)

simplify63.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

972×	`fma-def_binary64`
722×	`fma-neg_binary64`
154×	`cancel-sign-sub-inv_binary64`
107×	`distribute-rgt-in_binary64`
83×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	32	14
2	69	12
3	160	12
4	298	9
5	418	9
6	666	9
7	960	9
8	1262	9
9	1473	9
10	1531	9
11	1530	9
12	1536	9
13	1536	9
14	1401	9

prune3.0ms (0.2%)

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 x (fma.f64 x 9 -12) 3)
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Compiler

Compiled 65 to 50 computations (23.1% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 9 -12)
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(fma.f64 x (fma.f64 x 9 -12) 3)
2.0ms	(fma.f64 x 9 -12)

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 x (fma.f64 x 9 -12) 3)
0.0ms	(fma.f64 x 9 -12)

simplify59.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

785×	`associate-+l+_binary64`
415×	`fma-neg_binary64`
321×	`distribute-lft-in_binary64`
321×	`distribute-rgt-in_binary64`
225×	`distribute-rgt-out_binary64`

Counts

44 → 37

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	431
1	63	344
2	120	342
3	378	342
4	1764	342
5	4979	342
6	5271	342

prune30.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	35	4	39

Error

0.0b

Counts

39 → 4

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	0.8b	(*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Compiler

Compiled 455 to 350 computations (23.1% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.2b	(*.f64 9 (pow.f64 x 2))

series5.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

3.0ms	(*.f64 9 (pow.f64 x 2))
3.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

rewrite13.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`
7×	`add-log-exp_binary64`

Counts

2 → 51

Calls

2 calls:

7.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
4.0ms	(*.f64 9 (pow.f64 x 2))

simplify72.0ms (4%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-l_binary64`
410×	`associate-r_binary64`
379×	`fma-neg_binary64`
297×	`cancel-sign-sub-inv_binary64`
252×	`fma-def_binary64`

Counts

57 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	101	880
1	216	651
2	609	587
3	2814	561
4	4082	561
5	4830	561

prune71.0ms (3.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	88	4	92

Error

0.0b

Counts

92 → 4

Alt Table

Status	Error	Program
▶	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
	0.2b	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

Compiler

Compiled 1556 to 1245 computations (20% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
✓	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
✓	0.2b	(.f64 (.f64 x 3) x)

series9.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(.f64 (.f64 x 3) x)
3.0ms	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
3.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

rewrite19.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

3 → 61

Calls

3 calls:

9.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
4.0ms	(.f64 (.f64 x 3) x)
4.0ms	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))

simplify80.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

636×	`fma-neg_binary64`
363×	`fma-def_binary64`
281×	`+-commutative_binary64`
278×	`distribute-rgt-in_binary64`
273×	`distribute-lft-in_binary64`

Counts

97 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1328
1	302	1147
2	889	982
3	2422	980
4	4233	980
5	5064	980

prune114.0ms (6.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	111	5	116

Error

Counts

116 → 5

Alt Table

Status	Error	Program
	0.9b	(.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (+.f64 (-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4)) 1)))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
▶	0.2b	(.f64 3 (+.f64 (-.f64 (.f64 (sqrt.f64 (.f64 (.f64 x 3) x)) (sqrt.f64 (.f64 (.f64 x 3) x))) (*.f64 x 4)) 1))
✓	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Compiler

Compiled 2166 to 1676 computations (22.6% saved)

localize10.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (sqrt.f64 (.f64 (.f64 x 3) x)) (sqrt.f64 (.f64 (.f64 x 3) x))) (*.f64 x 4)) 1))
	0.2b	(.f64 (.f64 x 3) x)
✓	0.3b	(.f64 (sqrt.f64 (.f64 (.f64 x 3) x)) (sqrt.f64 (.f64 (*.f64 x 3) x)))
✓	15.2b	(sqrt.f64 (.f64 (.f64 x 3) x))

series17.0ms (0.9%)

Counts

3 → 36

Calls

3 calls:

7.0ms

(*.f64 (sqrt.f64 (*.f64 (*.f64 x 3) x)) (sqrt.f64 (*.f64 (*.f64 x 3) x)))

7.0ms

(*.f64 3 (+.f64 (-.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 x 3) x)) (sqrt.f64 (*.f64 (*.f64 x 3) x))) (*.f64 x 4)) 1))

3.0ms

(sqrt.f64 (*.f64 (*.f64 x 3) x))

rewrite38.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`pow1_binary64`
75×	`pow-prod-down_binary64`
63×	`sqrt-pow1_binary64`
17×	`pow-prod-up_binary64`
13×	`add-sqr-sqrt_binary64`

Counts

3 → 107

Calls

3 calls:

16.0ms

(*.f64 3 (+.f64 (-.f64 (*.f64 (sqrt.f64 (*.f64 (*.f64 x 3) x)) (sqrt.f64 (*.f64 (*.f64 x 3) x))) (*.f64 x 4)) 1))

9.0ms

(*.f64 (sqrt.f64 (*.f64 (*.f64 x 3) x)) (sqrt.f64 (*.f64 (*.f64 x 3) x)))

5.0ms

(sqrt.f64 (*.f64 (*.f64 x 3) x))

simplify98.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

624×	`unswap-sqr_binary64`
290×	`exp-prod_binary64`
262×	`distribute-rgt-in_binary64`
255×	`distribute-lft-in_binary64`
239×	`+-commutative_binary64`

Counts

143 → 131

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	107	1787
1	242	1351
2	715	1219
3	2156	1113
4	4074	1059
5	4694	1059
6	4931	1059

prune202.0ms (11.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	216	5	221

Error

Counts

221 → 5

Alt Table

Status	Error	Program
	0.9b	(.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (+.f64 (-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4)) 1)))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
✓	0.2b	(.f64 3 (+.f64 (-.f64 (.f64 (sqrt.f64 (.f64 (.f64 x 3) x)) (sqrt.f64 (.f64 (.f64 x 3) x))) (*.f64 x 4)) 1))
✓	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Compiler

Compiled 5430 to 4168 computations (23.2% saved)

regimes228.0ms (12.5%)

Accuracy

Total 0.1b remaining (88.6%)

Threshold costs 0.1b (88.6%)

Counts

50 → 1

Compiler

Compiled 2866 to 2327 computations (18.8% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	12	11
2	13	11
3	12	11

end1.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

sample566.0ms (31.1%)

Algorithm

1×

intervals

Results

324.0ms

8000×

body

128

valid

Compiler

Compiled 99 to 79 computations (20.2% saved)

Details

analyze7.0ms (0.4%)

sample86.0ms (4.7%)

simplify63.0ms (3.5%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite2.0ms (0.1%)

simplify59.0ms (3.3%)

prune30.0ms (1.6%)

localize7.0ms (0.4%)

series5.0ms (0.3%)

rewrite13.0ms (0.7%)

simplify72.0ms (4%)

prune71.0ms (3.9%)

localize7.0ms (0.4%)

series9.0ms (0.5%)

rewrite19.0ms (1%)

simplify80.0ms (4.4%)

prune114.0ms (6.2%)

localize10.0ms (0.6%)

series17.0ms (0.9%)

rewrite38.0ms (2.1%)

simplify98.0ms (5.4%)

prune202.0ms (11.1%)

regimes228.0ms (12.5%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample566.0ms (31.1%)

Profiling