Details

analyze4.0ms (0.2%)

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)

sample828.0ms (43.9%)

Results

742.0ms	8256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify64.0ms (3.4%)

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)
	0.2b	(.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)
1.0ms	(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)

simplify61.0ms (3.2%)

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

prune32.0ms (1.7%)

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)
	0.2b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
	1.9b	(expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))

Compiler

Compiled 439 to 338 computations (23% saved)

localize6.0ms (0.3%)

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:

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

rewrite10.0ms (0.5%)

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:

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

simplify76.0ms (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

prune66.0ms (3.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	2	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 (+.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 (.f64 x 3) x) (.f64 x 4)) 1))
	1.9b	(expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))

Compiler

Compiled 1548 to 1239 computations (20% saved)

localize7.0ms (0.3%)

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)

series8.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
2.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
2.0ms	(.f64 (.f64 x 3) x)

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:

10.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
4.0ms	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
4.0ms	(.f64 (.f64 x 3) x)

simplify74.0ms (3.9%)

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

prune88.0ms (4.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

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

Error

Counts

116 → 5

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)
✓	0.2b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
	1.9b	(expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))
▶	0.2b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1)))

Compiler

Compiled 2148 to 1664 computations (22.5% saved)

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series14.0ms (0.7%)

Counts

2 → 24

Calls

2 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1)))
5.0ms	(.f64 (cbrt.f64 3) (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

rewrite22.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`cbrt-unprod_binary64`
9×	`add-cbrt-cube_binary64`

Counts

2 → 59

Calls

2 calls:

11.0ms	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1)))
8.0ms	(.f64 (cbrt.f64 3) (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

simplify91.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

673×	`distribute-rgt-in_binary64`
661×	`distribute-lft-in_binary64`
614×	`fma-neg_binary64`
266×	`fma-def_binary64`
244×	`*-commutative_binary64`

Counts

83 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	107	2010
1	286	1428
2	868	1167
3	3364	1157
4	4756	1157
5	5198	1157

prune163.0ms (8.6%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	168	5	173

Error

Counts

173 → 5

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)
✓	0.2b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
	1.9b	(expm1.f64 (log1p.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))
✓	0.2b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1)))

Compiler

Compiled 4326 to 3628 computations (16.1% saved)

regimes155.0ms (8.2%)

Accuracy

Total 0.1b remaining (85.5%)

Threshold costs 0.1b (85.5%)

Counts

41 → 1

Compiler

Compiled 2338 to 1947 computations (16.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

end71.0ms (3.7%)

Compiler: Compiled 83 to 67 computations (19.3% saved)

Details

analyze4.0ms (0.2%)

sample828.0ms (43.9%)

simplify64.0ms (3.4%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0.1%)

simplify61.0ms (3.2%)

prune32.0ms (1.7%)

localize6.0ms (0.3%)

series5.0ms (0.3%)

rewrite10.0ms (0.5%)

simplify76.0ms (4%)

prune66.0ms (3.5%)

localize7.0ms (0.3%)

series8.0ms (0.4%)

rewrite19.0ms (1%)

simplify74.0ms (3.9%)

prune88.0ms (4.7%)

localize10.0ms (0.5%)

series14.0ms (0.7%)

rewrite22.0ms (1.2%)

simplify91.0ms (4.8%)

prune163.0ms (8.6%)

regimes155.0ms (8.2%)

simplify2.0ms (0.1%)

end71.0ms (3.7%)

Profiling