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
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)

sample723.0ms (39.5%)

Results

707.0ms	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 22 to 18 computations (18.2% saved)

preprocess25.0ms (1.4%)

Algorithm

2×	egg-herbie

Rules

271×	`fma-def_binary64`
256×	`fma-neg_binary64`
75×	`cancel-sign-sub-inv_binary64`
54×	`sub-neg_binary64`
30×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	65	11
3	147	11
4	291	9
5	486	9
6	718	9
7	1049	9
8	1166	9
9	1185	9
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 8 computations (20% saved)

simplify18.0ms (1%)

Algorithm

1×	egg-herbie

Rules

271×	`fma-def_binary64`
256×	`fma-neg_binary64`
75×	`cancel-sign-sub-inv_binary64`
54×	`sub-neg_binary64`
30×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	65	11
3	147	11
4	291	9
5	486	9
6	718	9
7	1049	9
8	1166	9
9	1185	9

Stop Event

1×

saturated

Counts

1 → 2

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

0.1b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 53 to 41 computations (22.6% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series6.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

1.0ms	(.f64 x (+.f64 253/1000 (.f64 x 3/25)))	x	-inf
1.0ms	(.f64 x (+.f64 253/1000 (.f64 x 3/25)))	x	inf
1.0ms	(.f64 x (+.f64 253/1000 (.f64 x 3/25)))	x	0
1.0ms	(+.f64 253/1000 (*.f64 x 3/25))	x	-inf
1.0ms	(*.f64 x 3/25)	x	0

rewrite47.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

769×	`log1p-expm1-u_binary64`
769×	`expm1-log1p-u_binary64`
275×	`prod-diff_binary64`
79×	`add-sqr-sqrt_binary64`
75×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	158	17
2	2059	17

Stop Event

1×	node limit

Counts

3 → 73

simplify69.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

543×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
370×	`sqr-pow_binary64`
366×	`fma-def_binary64`
301×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	237
1	22	219
2	36	192
3	62	192
4	155	192
5	477	192
6	1677	192
7	2931	192
8	3135	192
9	3348	192
10	3568	192
11	3873	192
12	4275	192
13	4785	192

Stop Event

1×	node limit

Counts

109 → 82

prune77.0ms (4.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	79	5	84

Error

0.0b

Counts

84 → 5

Alt Table

Status	Error	Program
	15.0b	(-.f64 1 (/.f64 (-.f64 (.f64 (.f64 x 253/1000) (.f64 x 253/1000)) (.f64 (.f64 x (.f64 x 3/25)) (.f64 x (.f64 x 3/25)))) (-.f64 (.f64 x 253/1000) (.f64 x (*.f64 x 3/25)))))
	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
▶	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
	21.0b	(-.f64 1 (pow.f64 (sqrt.f64 (*.f64 x (fma.f64 x 3/25 253/1000))) 2))
	0.4b	(-.f64 1 (pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 3/25 253/1000))) 3))

Compiler

Compiled 1257 to 1013 computations (19.4% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(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

6 calls:

1.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)	x	inf
1.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)	x	-inf
1.0ms	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)	x	0
1.0ms	(fma.f64 x -3/25 -253/1000)	x	-inf
0.0ms	(fma.f64 x -3/25 -253/1000)	x	inf

rewrite35.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	136	14
2	1424	14

Stop Event

1×	node limit

Counts

2 → 66

simplify34.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

396×	`associate-l_binary64`
391×	`fma-def_binary64`
312×	`distribute-rgt-neg-in_binary64`
301×	`unswap-sqr_binary64`
271×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	222
1	51	204
2	112	156
3	239	144
4	834	144
5	2839	144
6	4254	144

Stop Event

1×	node limit

Counts

90 → 80

prune73.0ms (4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	80	5	85

Error

0.0b

Counts

85 → 5

Alt Table

Status	Error	Program
	15.0b	(-.f64 1 (/.f64 (-.f64 (.f64 (.f64 x 253/1000) (.f64 x 253/1000)) (.f64 (.f64 x (.f64 x 3/25)) (.f64 x (.f64 x 3/25)))) (-.f64 (.f64 x 253/1000) (.f64 x (*.f64 x 3/25)))))
▶	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
	0.4b	(-.f64 1 (pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 3/25 253/1000))) 3))
	51.8b	(fma.f64 x (pow.f64 (sqrt.f64 (fma.f64 x -3/25 -253/1000)) 2) 1)

Compiler

Compiled 1148 to 917 computations (20.1% saved)

localize10.0ms (0.5%)

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))

series7.0ms (0.4%)

Counts

3 → 3

Calls

9 calls:

1.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))	x	-inf
1.0ms	(+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x))	x	inf
1.0ms	(*.f64 3/25 (pow.f64 x 2))	x	0
1.0ms	(*.f64 3/25 (pow.f64 x 2))	x	-inf
1.0ms	(*.f64 3/25 (pow.f64 x 2))	x	inf

rewrite52.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

852×	`log1p-expm1-u_binary64`
852×	`expm1-log1p-u_binary64`
92×	`add-sqr-sqrt_binary64`
89×	`add-cbrt-cube_binary64`
88×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	196	22
2	2348	22

Stop Event

1×	node limit

Counts

3 → 65

simplify57.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

626×	`sqr-pow_binary64`
513×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
285×	`cube-prod_binary64`
280×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	15	18
2	26	18
3	51	18
4	124	18
5	367	18
6	1384	18
7	2272	18
8	2436	18
9	2650	18
10	2870	18
11	3171	18
12	3571	18
13	4057	18
14	4618	18

Stop Event

1×	node limit

Counts

68 → 68

prune60.0ms (3.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	68	5	73

Error

0.0b

Counts

73 → 5

Alt Table

Status	Error	Program
	15.0b	(-.f64 1 (/.f64 (-.f64 (.f64 (.f64 x 253/1000) (.f64 x 253/1000)) (.f64 (.f64 x (.f64 x 3/25)) (.f64 x (.f64 x 3/25)))) (-.f64 (.f64 x 253/1000) (.f64 x (*.f64 x 3/25)))))
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
▶	0.4b	(-.f64 1 (pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 3/25 253/1000))) 3))
	51.8b	(fma.f64 x (pow.f64 (sqrt.f64 (fma.f64 x -3/25 -253/1000)) 2) 1)

Compiler

Compiled 1234 to 893 computations (27.6% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x 3/25 253/1000)
✓	0.2b	(*.f64 x (fma.f64 x 3/25 253/1000))
✓	0.6b	(cbrt.f64 (*.f64 x (fma.f64 x 3/25 253/1000)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 3/25 253/1000))) 3)

series41.0ms (2.2%)

Counts

4 → 24

Calls

12 calls:

18.0ms	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 3/25 253/1000))) 3)	x	-inf
9.0ms	(cbrt.f64 (*.f64 x (fma.f64 x 3/25 253/1000)))	x	-inf
4.0ms	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 3/25 253/1000))) 3)	x	0
3.0ms	(pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 3/25 253/1000))) 3)	x	inf
1.0ms	(cbrt.f64 (*.f64 x (fma.f64 x 3/25 253/1000)))	x	0

rewrite50.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

679×	`log1p-expm1-u_binary64`
679×	`expm1-log1p-u_binary64`
320×	`log-prod_binary64`
135×	`expm1-udef_binary64`
135×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
1	184	31
2	1862	31

Stop Event

1×	node limit

Counts

4 → 118

simplify65.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

542×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
370×	`sqr-pow_binary64`
366×	`fma-def_binary64`
312×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	189
1	22	171
2	36	144
3	62	144
4	154	144
5	471	144
6	1687	144
7	2949	144
8	3153	144
9	3366	144
10	3586	144
11	3890	144
12	4290	144
13	4798	144

Stop Event

1×	node limit

Counts

142 → 109

prune95.0ms (5.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	109	5	114

Error

0.0b

Counts

114 → 5

Alt Table

Status	Error	Program
	15.0b	(-.f64 1 (/.f64 (-.f64 (.f64 (.f64 x 253/1000) (.f64 x 253/1000)) (.f64 (.f64 x (.f64 x 3/25)) (.f64 x (.f64 x 3/25)))) (-.f64 (.f64 x 253/1000) (.f64 x (*.f64 x 3/25)))))
✓	0.1b	(-.f64 1 (+.f64 (.f64 3/25 (pow.f64 x 2)) (.f64 253/1000 x)))
✓	0.1b	(fma.f64 x (fma.f64 x -3/25 -253/1000) 1)
✓	0.4b	(-.f64 1 (pow.f64 (cbrt.f64 (*.f64 x (fma.f64 x 3/25 253/1000))) 3))
	51.8b	(fma.f64 x (pow.f64 (sqrt.f64 (fma.f64 x -3/25 -253/1000)) 2) 1)

Compiler

Compiled 1774 to 1448 computations (18.4% saved)

regimes180.0ms (9.9%)

Accuracy

Total 0.1b remaining (69.2%)

Threshold costs 0.1b (69.2%)

Counts

63 → 1

Compiler

Compiled 2482 to 1953 computations (21.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-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	15	14
2	19	14
3	21	14
4	22	14

Stop Event

1×

saturated

end76.0ms (4.2%)

Stop Event

1×

fuel

Compiler

Compiled 97 to 74 computations (23.7% saved)

Details

analyze4.0ms (0.2%)

sample723.0ms (39.5%)

preprocess25.0ms (1.4%)

simplify18.0ms (1%)

prune3.0ms (0.2%)

localize5.0ms (0.3%)

series6.0ms (0.3%)

rewrite47.0ms (2.5%)

simplify69.0ms (3.8%)

prune77.0ms (4.2%)

localize5.0ms (0.3%)

series4.0ms (0.2%)

rewrite35.0ms (1.9%)

simplify34.0ms (1.8%)

prune73.0ms (4%)

localize10.0ms (0.5%)

series7.0ms (0.4%)

rewrite52.0ms (2.8%)

simplify57.0ms (3.1%)

prune60.0ms (3.3%)

localize7.0ms (0.4%)

series41.0ms (2.2%)

rewrite50.0ms (2.7%)

simplify65.0ms (3.5%)

prune95.0ms (5.2%)

regimes180.0ms (9.9%)

simplify2.0ms (0.1%)

end76.0ms (4.2%)

Profiling