Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 15 to 12 computations (20% saved)

sample640.0ms (34%)

Infinites

26.2% of outputs are infinite.

Results

542.0ms

8256×

body

128

valid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify61.0ms (3.3%)

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

prune4.0ms (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
	0.6b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
▶	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

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)

series5.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

rewrite1.0ms (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)

simplify62.0ms (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

prune33.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	34	5	39

Error

Counts

39 → 5

Alt Table

Status	Error	Program
	0.6b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
	0.6b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
	0.6b	(*.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	(fma.f64 x (fma.f64 x 9 -12) 3)
▶	0.3b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 x 9 -12)) (cbrt.f64 (fma.f64 x 9 -12))) (cbrt.f64 (fma.f64 x 9 -12))) 3)

Compiler

Compiled 497 to 384 computations (22.7% saved)

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 x 9 -12)) (cbrt.f64 (fma.f64 x 9 -12))) (cbrt.f64 (fma.f64 x 9 -12))) 3)
✓	0.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 x 9 -12)) (cbrt.f64 (fma.f64 x 9 -12))) (cbrt.f64 (fma.f64 x 9 -12)))
✓	0.7b	(*.f64 (cbrt.f64 (fma.f64 x 9 -12)) (cbrt.f64 (fma.f64 x 9 -12)))
✓	1.2b	(cbrt.f64 (fma.f64 x 9 -12))

series17.0ms (0.9%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 (fma.f64 x 9 -12)) (cbrt.f64 (fma.f64 x 9 -12)))
5.0ms	(cbrt.f64 (fma.f64 x 9 -12))
4.0ms	(fma.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 x 9 -12)) (cbrt.f64 (fma.f64 x 9 -12))) (cbrt.f64 (fma.f64 x 9 -12))) 3)
2.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 x 9 -12)) (cbrt.f64 (fma.f64 x 9 -12))) (cbrt.f64 (fma.f64 x 9 -12)))

rewrite18.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
25×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
15×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 (fma.f64 x 9 -12)) (cbrt.f64 (fma.f64 x 9 -12))) (cbrt.f64 (fma.f64 x 9 -12)))
4.0ms	(*.f64 (cbrt.f64 (fma.f64 x 9 -12)) (cbrt.f64 (fma.f64 x 9 -12)))
1.0ms	(cbrt.f64 (fma.f64 x 9 -12))
0.0ms	(fma.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 x 9 -12)) (cbrt.f64 (fma.f64 x 9 -12))) (cbrt.f64 (fma.f64 x 9 -12))) 3)

simplify100.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-neg_binary64`
427×	`fma-def_binary64`
242×	`*-commutative_binary64`
235×	`cancel-sign-sub-inv_binary64`
152×	`distribute-rgt-in_binary64`

Counts

151 → 196

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	2758
1	483	2496
2	1392	2124
3	4031	2081
4	4961	2081

prune285.0ms (15.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	274	5	279

Error

Counts

279 → 5

Alt Table

Status	Error	Program
	0.6b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
▶	0.6b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
	0.6b	(*.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	(fma.f64 x (fma.f64 x 9 -12) 3)
✓	0.3b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 x 9 -12)) (cbrt.f64 (fma.f64 x 9 -12))) (cbrt.f64 (fma.f64 x 9 -12))) 3)

Compiler

Compiled 7914 to 6563 computations (17.1% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 9 (pow.f64 x 2))
✓	0.4b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

series5.0ms (0.3%)

Counts

2 → 6

Calls

2 calls:

3.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
2.0ms	(*.f64 9 (pow.f64 x 2))

rewrite12.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`add-exp-log_binary64`
7×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64`

Counts

2 → 51

Calls

2 calls:

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

simplify71.0ms (3.8%)

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

prune90.0ms (4.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	88	5	93

Error

Counts

93 → 5

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 x 9 -12)) (cbrt.f64 (fma.f64 x 9 -12))) (cbrt.f64 (fma.f64 x 9 -12))) 3)
	0.6b	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))
▶	0.6b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
✓	0.6b	(-.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 1577 to 1257 computations (20.3% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
✓	0.1b	(.f64 (.f64 x 3) x)
✓	0.4b	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))

series8.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

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))
2.0ms	(.f64 (.f64 x 3) x)

rewrite24.0ms (1.3%)

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:

8.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
7.0ms	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
4.0ms	(.f64 (.f64 x 3) x)

simplify78.0ms (4.1%)

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 → 110

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

prune103.0ms (5.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	110	5	115

Error

Counts

115 → 5

Alt Table

Status	Error	Program
✓	0.3b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 x 9 -12)) (cbrt.f64 (fma.f64 x 9 -12))) (cbrt.f64 (fma.f64 x 9 -12))) 3)
	0.6b	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))
✓	0.6b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
✓	0.6b	(-.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 2086 to 1617 computations (22.5% saved)

regimes143.0ms (7.6%)

Accuracy

Total 0.1b remaining (88.4%)

Threshold costs 0.1b (88.4%)

Counts

37 → 1

Compiler

Compiled 1832 to 1473 computations (19.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end92.0ms (4.9%)

Compiler: Compiled 85 to 67 computations (21.2% saved)

Details

analyze1.0ms (0%)

sample640.0ms (34%)

simplify61.0ms (3.3%)

prune4.0ms (0.2%)

localize4.0ms (0.2%)

series5.0ms (0.3%)

rewrite1.0ms (0.1%)

simplify62.0ms (3.3%)

prune33.0ms (1.7%)

localize9.0ms (0.5%)

series17.0ms (0.9%)

rewrite18.0ms (1%)

simplify100.0ms (5.3%)

prune285.0ms (15.1%)

localize7.0ms (0.4%)

series5.0ms (0.3%)

rewrite12.0ms (0.6%)

simplify71.0ms (3.8%)

prune90.0ms (4.8%)

localize7.0ms (0.4%)

series8.0ms (0.4%)

rewrite24.0ms (1.3%)

simplify78.0ms (4.1%)

prune103.0ms (5.5%)

regimes143.0ms (7.6%)

simplify3.0ms (0.1%)

end92.0ms (4.9%)

Profiling