Details

analyze2.5s (24.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
2.3%	97.4%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
29.7%	70%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.3s (22.1%)

Results

2.0s	8256×	body	128	valid
160.0ms	718×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify127.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1405×	`fma-def_binary64`
906×	`div-sub_binary64`
613×	`distribute-rgt-in_binary64`
583×	`fma-neg_binary64`
525×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	22	14
2	43	14
3	82	14
4	164	14
5	304	14
6	655	14
7	1590	14
8	3046	14
9	2781	14
10	2954	14
11	3028	14
12	3116	14
13	4289	14
14	5187	14

prune9.0ms (0.1%)

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

1.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
▶	1.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

Compiler

Compiled 88 to 49 computations (44.3% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	1.9b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

series207.0ms (2%)

Counts

3 → 144

Calls

3 calls:

104.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
66.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
37.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite130.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

553×	`fma-def_binary64`
280×	`fma-neg_binary64`
254×	`expm1-udef_binary64`
254×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`

Counts

3 → 129

Calls

3 calls:

124.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
124.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
124.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	258	37
2	3854	37
3	5479	37
0	0	0
1	0	0

simplify195.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

717×	`cancel-sign-sub-inv_binary64`
661×	`times-frac_binary64`
630×	`fma-neg_binary64`
450×	`sub-neg_binary64`
213×	`associate--l+_binary64`

Counts

273 → 239

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	202	4438
1	594	4195
2	2193	3525
3	4362	3513
4	5027	3513

prune396.0ms (3.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	236	3	239
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	237	4	241

Error

Counts

241 → 4

Alt Table

Status	Error	Program
	10.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
✓	1.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
▶	1.2b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
	28.9b	(fma.f64 (/.f64 y (sqrt.f64 (-.f64 z a))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a))) x)

Compiler

Compiled 5680 to 1866 computations (67.1% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	1.9b	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))

series210.0ms (2%)

Counts

3 → 144

Calls

3 calls:

93.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
70.0ms	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))
46.0ms	(/.f64 (-.f64 z a) (-.f64 z t))

rewrite134.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

294×	`fma-neg_binary64`
260×	`expm1-udef_binary64`
260×	`log1p-udef_binary64`
142×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`

Counts

3 → 132

Calls

3 calls:

128.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
128.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
128.0ms	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	264	37
2	4092	37
3	5219	37
0	0	0
1	0	0

simplify221.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

820×	`times-frac_binary64`
711×	`cancel-sign-sub-inv_binary64`
596×	`fma-neg_binary64`
435×	`sub-neg_binary64`
210×	`associate--l+_binary64`

Counts

276 → 243

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	215	4438
1	619	4195
2	2299	4075
3	4938	4075
4	5336	4075

prune329.0ms (3.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	243	0	243
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	243	4	247

Error

Counts

247 → 4

Alt Table

Status	Error	Program
▶	10.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
✓	1.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	1.2b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
	28.9b	(fma.f64 (/.f64 y (sqrt.f64 (-.f64 z a))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a))) x)

Compiler

Compiled 6029 to 1924 computations (68.1% saved)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 z t))
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
✓	10.7b	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

series187.0ms (1.8%)

Counts

3 → 144

Calls

3 calls:

104.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
70.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))
12.0ms	(*.f64 y (-.f64 z t))

rewrite122.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

521×	`fma-def_binary64`
265×	`fma-neg_binary64`
250×	`expm1-udef_binary64`
250×	`log1p-udef_binary64`
136×	`add-sqr-sqrt_binary64`

Counts

3 → 130

Calls

3 calls:

118.0ms	(*.f64 y (-.f64 z t))
118.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
118.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	255	36
2	3768	34
3	5334	34
0	0	0
1	0	0

simplify186.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

676×	`fma-def_binary64`
544×	`times-frac_binary64`
522×	`cancel-sign-sub-inv_binary64`
479×	`associate-/l*_binary64`
455×	`fma-neg_binary64`

Counts

274 → 213

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	147	3581
1	429	3338
2	1535	2828
3	4581	2826
4	4994	2826

prune262.0ms (2.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	213	4	217

Error

Counts

217 → 4

Alt Table

Status	Error	Program
✓	10.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
✓	1.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	1.2b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
▶	28.9b	(fma.f64 (/.f64 y (sqrt.f64 (-.f64 z a))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a))) x)

Compiler

Compiled 4761 to 1420 computations (70.2% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 z a))
✓	0.1b	(/.f64 y (sqrt.f64 (-.f64 z a)))
✓	0.2b	(fma.f64 (/.f64 y (sqrt.f64 (-.f64 z a))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a))) x)
✓	0.2b	(/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a)))

series651.0ms (6.3%)

Counts

4 → 95

Calls

4 calls:

352.0ms	(fma.f64 (/.f64 y (sqrt.f64 (-.f64 z a))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a))) x)
149.0ms	(/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a)))
113.0ms	(/.f64 y (sqrt.f64 (-.f64 z a)))
36.0ms	(sqrt.f64 (-.f64 z a))

rewrite207.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

389×	`fma-def_binary64`
259×	`expm1-udef_binary64`
259×	`log1p-udef_binary64`
213×	`fma-neg_binary64`
142×	`add-sqr-sqrt_binary64`

Counts

4 → 128

Calls

4 calls:

200.0ms	(sqrt.f64 (-.f64 z a))
200.0ms	(/.f64 y (sqrt.f64 (-.f64 z a)))
200.0ms	(fma.f64 (/.f64 y (sqrt.f64 (-.f64 z a))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a))) x)
200.0ms	(/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	51
1	270	43
2	3835	43
3	5220	43
0	0	0
1	0	0

simplify176.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

609×	`cancel-sign-sub-inv_binary64`
266×	`sub-neg_binary64`
260×	`times-frac_binary64`
216×	`fma-def_binary64`
190×	`associate-r_binary64`

Counts

223 → 207

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	266	2908
1	892	2857
2	3577	2846
3	5033	2846

prune365.0ms (3.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	245	4	249

Error

Counts

249 → 4

Alt Table

Status	Error	Program
✓	10.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
✓	1.3b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
✓	1.2b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
✓	28.9b	(fma.f64 (/.f64 y (sqrt.f64 (-.f64 z a))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 z a))) x)

Compiler

Compiled 6806 to 2513 computations (63.1% saved)

regimes1.2s (11.8%)

Accuracy

Total 1.1b remaining (98.5%)

Threshold costs 0b (0%)

Counts

73 → 1

Compiler

Compiled 10570 to 6710 computations (36.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	16	16
2	24	16
3	28	16
4	30	16
5	30	16

end129.0ms (1.2%)

Compiler: Compiled 101 to 61 computations (39.6% saved)

Details

analyze2.5s (24.4%)

sample2.3s (22.1%)

simplify127.0ms (1.2%)

prune9.0ms (0.1%)

localize16.0ms (0.2%)

series207.0ms (2%)

rewrite130.0ms (1.3%)

simplify195.0ms (1.9%)

prune396.0ms (3.8%)

localize15.0ms (0.1%)

series210.0ms (2%)

rewrite134.0ms (1.3%)

simplify221.0ms (2.1%)

prune329.0ms (3.2%)

localize15.0ms (0.1%)

series187.0ms (1.8%)

rewrite122.0ms (1.2%)

simplify186.0ms (1.8%)

prune262.0ms (2.5%)

localize18.0ms (0.2%)

series651.0ms (6.3%)

rewrite207.0ms (2%)

simplify176.0ms (1.7%)

prune365.0ms (3.5%)

regimes1.2s (11.8%)

simplify6.0ms (0.1%)

end129.0ms (1.2%)

Profiling