Details

analyze5.0ms (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
75%	25%	0%	4
75%	12.5%	12.5%	5
75%	6.2%	18.8%	6
75%	3.1%	21.9%	7
75%	1.6%	23.5%	8
75%	0.8%	24.3%	9
75%	0.4%	24.6%	10
75%	0.2%	24.8%	11
75%	0.1%	24.9%	12
75%	0%	24.9%	13
75%	0%	25%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample747.0ms (34.2%)

Results

689.0ms	8256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify23.0ms (1%)

Algorithm

1×	egg-herbie

Rules

271×	`fma-def_binary64`
257×	`fma-neg_binary64`
76×	`cancel-sign-sub-inv_binary64`
55×	`sub-neg_binary64`
32×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	54	11
3	122	11
4	222	9
5	361	9
6	423	9
7	587	9
8	645	9
9	664	9
10	593	9

prune5.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

Compiler

Compiled 33 to 25 computations (24.2% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x -3/25 -253/1000)
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
2.0ms	(fma.f64 x -3/25 -253/1000)

rewrite43.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

543×	`log1p-expm1-u_binary64`
543×	`expm1-log1p-u_binary64`
262×	`unpow-prod-down_binary64`
236×	`log-prod_binary64`
160×	`pow2_binary64`

Counts

2 → 66

Calls

2 calls:

42.0ms	(fma.f64 x -3/25 -253/1000)
42.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	136	14
2	1384	14
3	4894	14
0	0	0
1	0	0

simplify172.0ms (7.9%)

Algorithm

1×	egg-herbie

Rules

1932×	`fma-neg_binary64`
761×	`fma-def_binary64`
715×	`distribute-rgt-neg-in_binary64`
558×	`cancel-sign-sub-inv_binary64`
409×	`associate-l_binary64`

Counts

90 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	222
1	51	204
2	105	156
3	220	144
4	603	144
5	1495	144
6	2078	144
7	2716	144
8	2868	144
9	2147	144
10	2292	144
11	3846	144
12	4135	144
13	4291	144
14	4803	144
15	4953	144
16	4838	144

prune62.0ms (2.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	4	81

Error

0.0b

Counts

81 → 4

Alt Table

Status	Error	Program
	8.1b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3)) 1)
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
▶	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
	0.4b	(fma.f64 x (*.f64 (cbrt.f64 (fma.f64 x -3/25 -253/1000)) (pow.f64 (cbrt.f64 (fma.f64 x -3/25 -253/1000)) 2)) 1)

Compiler

Compiled 1094 to 879 computations (19.7% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
✓	0.1b	(*.f64 253/1000 x)
✓	0.2b	(*.f64 3/25 (pow.f64 x 2))

series8.0ms (0.4%)

Counts

3 → 3

Calls

3 calls:

4.0ms	(*.f64 3/25 (pow.f64 x 2))
3.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
1.0ms	(*.f64 253/1000 x)

rewrite51.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

852×	`log1p-expm1-u_binary64`
852×	`expm1-log1p-u_binary64`
92×	`add-sqr-sqrt_binary64`
88×	`add-log-exp_binary64`
87×	`add-cube-cbrt_binary64`

Counts

3 → 65

Calls

3 calls:

49.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))
49.0ms	(*.f64 253/1000 x)
49.0ms	(*.f64 3/25 (pow.f64 x 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	196	22
2	2172	22
3	5034	22
0	0	0
1	0	0

simplify161.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

1127×	`sqr-pow_binary64`
577×	`fabs-mul_binary64`
564×	`cube-prod_binary64`
541×	`pow-sqr_binary64`
523×	`associate-l_binary64`

Counts

68 → 68

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	15	18
2	25	18
3	48	18
4	103	18
5	258	18
6	800	18
7	1203	18
8	1308	18
9	1464	18
10	1644	18
11	1825	18
12	2048	18
13	2215	18
14	2634	18
15	3199	18
16	3885	18
17	4103	18
18	4347	18
19	4429	18
20	4462	18
21	4483	18
22	5052	18

prune60.0ms (2.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	67	5	72

Error

Counts

72 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
▶	0.1b	(-.f64 1 (+.f64 (pow.f64 (.f64 x (sqrt.f64 3/25)) 2) (.f64 253/1000 x)))
	8.1b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3)) 1)
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
	11.0b	(-.f64 1 (+.f64 (sqrt.f64 (.f64 9/625 (pow.f64 x 4))) (.f64 253/1000 x)))

Compiler

Compiled 1198 to 872 computations (27.2% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (.f64 x (sqrt.f64 3/25)) 2) (.f64 253/1000 x))
✓	0.0b	(*.f64 x (sqrt.f64 3/25))
	0.1b	(*.f64 253/1000 x)
✓	0.3b	(pow.f64 (*.f64 x (sqrt.f64 3/25)) 2)

series15.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(+.f64 (pow.f64 (.f64 x (sqrt.f64 3/25)) 2) (.f64 253/1000 x))
5.0ms	(pow.f64 (*.f64 x (sqrt.f64 3/25)) 2)
3.0ms	(*.f64 x (sqrt.f64 3/25))

rewrite88.0ms (4%)

Algorithm

2×	batch-egg-rewrite

Rules

433×	`log-prod_binary64`
313×	`fma-def_binary64`
249×	`pow2_binary64`
219×	`fma-neg_binary64`
174×	`expm1-udef_binary64`

Counts

3 → 113

Calls

3 calls:

86.0ms	(+.f64 (pow.f64 (.f64 x (sqrt.f64 3/25)) 2) (.f64 253/1000 x))
86.0ms	(*.f64 x (sqrt.f64 3/25))
86.0ms	(pow.f64 (*.f64 x (sqrt.f64 3/25)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	217	24
2	2370	24
3	4978	24
4	4910	24
0	0	0
1	0	0

simplify96.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

969×	`fma-def_binary64`
687×	`associate-l_binary64`
514×	`distribute-rgt-in_binary64`
488×	`associate-r_binary64`
318×	`sqr-pow_binary64`

Counts

149 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	388
1	25	273
2	44	264
3	107	246
4	314	246
5	1351	246
6	1682	246
7	1905	246
8	2304	246
9	2895	246
10	3944	246
11	4965	246
12	4894	246

prune109.0ms (5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	132	5	137

Error

Counts

137 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (pow.f64 (.f64 x (sqrt.f64 3/25)) 2) (.f64 253/1000 x)))
▶	8.1b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3)) 1)
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
	11.0b	(-.f64 1 (+.f64 (sqrt.f64 (.f64 9/625 (pow.f64 x 4))) (.f64 253/1000 x)))

Compiler

Compiled 2272 to 1709 computations (24.8% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x -3/25 -253/1000)
✓	0.1b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3)) 1)
✓	0.2b	(pow.f64 (fma.f64 x -3/25 -253/1000) 3)
✓	8.5b	(cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3))

series7.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

2.0ms	(pow.f64 (fma.f64 x -3/25 -253/1000) 3)
2.0ms	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3)) 1)
2.0ms	(cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3))

rewrite72.0ms (3.3%)

Algorithm

2×	batch-egg-rewrite

Rules

709×	`log1p-expm1-u_binary64`
709×	`expm1-log1p-u_binary64`
142×	`expm1-udef_binary64`
142×	`log1p-udef_binary64`
117×	`log-pow_binary64`

Counts

3 → 83

Calls

3 calls:

70.0ms	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3)) 1)
70.0ms	(pow.f64 (fma.f64 x -3/25 -253/1000) 3)
70.0ms	(cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
1	183	22
2	1826	22
3	4939	22
4	4789	22
0	0	0
1	0	0

simplify80.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

641×	`unsub-neg_binary64`
495×	`fma-def_binary64`
476×	`fma-neg_binary64`
397×	`distribute-rgt-neg-in_binary64`
360×	`cancel-sign-sub-inv_binary64`

Counts

119 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	403
1	121	375
2	327	311
3	858	276
4	2414	276
5	3055	276
6	4436	276
7	4975	276

prune115.0ms (5.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	147	5	152

Error

Counts

152 → 5

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
✓	0.1b	(-.f64 1 (+.f64 (pow.f64 (.f64 x (sqrt.f64 3/25)) 2) (.f64 253/1000 x)))
✓	8.1b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 x -3/25 -253/1000) 3)) 1)
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
	11.0b	(-.f64 1 (+.f64 (sqrt.f64 (.f64 9/625 (pow.f64 x 4))) (.f64 253/1000 x)))

Compiler

Compiled 2008 to 1628 computations (18.9% saved)

regimes98.0ms (4.5%)

Accuracy

Total 0.2b remaining (90.5%)

Threshold costs 0.2b (90.5%)

Counts

35 → 1

Compiler

Compiled 1072 to 849 computations (20.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	14
2	18	14
3	20	14
4	21	14
5	20	14

end132.0ms (6.1%)

Compiler: Compiled 79 to 63 computations (20.3% saved)

Details

analyze5.0ms (0.2%)

sample747.0ms (34.2%)

simplify23.0ms (1%)

prune5.0ms (0.2%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite43.0ms (2%)

simplify172.0ms (7.9%)

prune62.0ms (2.9%)

localize6.0ms (0.3%)

series8.0ms (0.4%)

rewrite51.0ms (2.3%)

simplify161.0ms (7.4%)

prune60.0ms (2.8%)

localize8.0ms (0.3%)

series15.0ms (0.7%)

rewrite88.0ms (4%)

simplify96.0ms (4.4%)

prune109.0ms (5%)

localize8.0ms (0.4%)

series7.0ms (0.3%)

rewrite72.0ms (3.3%)

simplify80.0ms (3.7%)

prune115.0ms (5.3%)

regimes98.0ms (4.5%)

simplify2.0ms (0.1%)

end132.0ms (6.1%)

Profiling