Details

analyze1.4s (16.4%)

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
0%	99.8%	0.2%	9
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
16.5%	83.2%	0.2%	13
25.9%	73.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.3s (14.4%)

Results

1.1s	8253×	body	128	valid
94.0ms	757×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify118.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1893×	`fma-neg_binary64`
867×	`div-sub_binary64`
749×	`fma-def_binary64`
696×	`distribute-rgt-in_binary64`
535×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	40	14
3	81	14
4	160	14
5	302	14
6	620	14
7	1528	14
8	2624	14
9	2858	14
10	3205	14
11	3392	14
12	3498	14
13	3533	14
14	5398	14

prune4.0ms (0%)

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
▶	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	12.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	2.7b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series55.0ms (0.6%)

Counts

2 → 84

Calls

2 calls:

35.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
20.0ms	(/.f64 t (-.f64 a z))

rewrite69.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

805×	`prod-diff_binary64`
218×	`log1p-udef_binary64`
119×	`add-sqr-sqrt_binary64`
113×	`log1p-expm1-u_binary64`
113×	`expm1-log1p-u_binary64`

Counts

2 → 58

Calls

2 calls:

67.0ms	(/.f64 t (-.f64 a z))
67.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	223	21
2	3080	21
3	5017	21
0	0	0
1	0	0

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Rules

636×	`times-frac_binary64`
600×	`fma-def_binary64`
499×	`associate-/l*_binary64`
465×	`fma-neg_binary64`
262×	`cancel-sign-sub-inv_binary64`

Counts

142 → 114

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	2438
1	357	2438
2	1354	2037
3	4700	2037
4	5053	2037

prune90.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	112	4	116

Error

0.0b

Counts

116 → 4

Alt Table

Status	Error	Program
▶	2.4b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
✓	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	33.7b	(pow.f64 (sqrt.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)) 2)

Compiler

Compiled 2431 to 784 computations (67.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 z (-.f64 a z))
✓	0.0b	(/.f64 y (-.f64 a z))
✓	0.0b	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
✓	3.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

series101.0ms (1.1%)

Counts

4 → 111

Calls

4 calls:

48.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
25.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
19.0ms	(/.f64 y (-.f64 a z))
9.0ms	(/.f64 z (-.f64 a z))

rewrite105.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

534×	`fma-def_binary64`
283×	`fma-neg_binary64`
254×	`egg-rr`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`

Counts

4 → 254

Calls

4 calls:

99.0ms	(/.f64 z (-.f64 a z))
99.0ms	(/.f64 y (-.f64 a z))
99.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
99.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	234	37
2	3586	37
3	5112	37
0	0	0
1	0	0

simplify124.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary64`
757×	`times-frac_binary64`
673×	`fma-neg_binary64`
495×	`cancel-sign-sub-inv_binary64`
329×	`sub-neg_binary64`

Counts

365 → 359

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	3449
1	508	3422
2	1922	2937
3	4520	2937
4	5001	2937

prune604.0ms (6.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	357	2	359
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	359	4	363

Error

Counts

363 → 4

Alt Table

Status	Error	Program
▶	2.6b	(+.f64 x (*.f64 t (/.f64 1 (/.f64 (-.f64 a z) (-.f64 y z)))))
	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	29.9b	(+.f64 x (pow.f64 (sqrt.f64 (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))) 2))
✓	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

Compiler

Compiled 9459 to 3102 computations (67.2% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a z) (-.f64 y z))
✓	0.5b	(/.f64 1 (/.f64 (-.f64 a z) (-.f64 y z)))
✓	3.3b	(*.f64 t (/.f64 1 (/.f64 (-.f64 a z) (-.f64 y z))))

series144.0ms (1.6%)

Counts

3 → 120

Calls

3 calls:

68.0ms	(*.f64 t (/.f64 1 (/.f64 (-.f64 a z) (-.f64 y z))))
41.0ms	(/.f64 1 (/.f64 (-.f64 a z) (-.f64 y z)))
35.0ms	(/.f64 (-.f64 a z) (-.f64 y z))

rewrite243.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

961×	`prod-diff_binary64`
306×	`egg-rr`
129×	`add-sqr-sqrt_binary64`
122×	`log1p-expm1-u_binary64`
122×	`expm1-log1p-u_binary64`

Counts

3 → 306

Calls

3 calls:

208.0ms	(/.f64 (-.f64 a z) (-.f64 y z))
208.0ms	(/.f64 1 (/.f64 (-.f64 a z) (-.f64 y z)))
208.0ms	(*.f64 t (/.f64 1 (/.f64 (-.f64 a z) (-.f64 y z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	250	33
2	3483	33
3	5368	33
0	0	0
1	0	0

simplify194.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

798×	`cancel-sign-sub-inv_binary64`
527×	`fma-neg_binary64`
488×	`sub-neg_binary64`
223×	`unsub-neg_binary64`
213×	`associate--l+_binary64`

Counts

426 → 408

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	229	3699
1	668	3618
2	2558	3092
3	4310	3080
4	5021	3080

prune645.0ms (7.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	408	0	408
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	408	4	412

Error

Counts

412 → 4

Alt Table

Status	Error	Program
✓	2.6b	(+.f64 x (*.f64 t (/.f64 1 (/.f64 (-.f64 a z) (-.f64 y z)))))
▶	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	29.9b	(+.f64 x (pow.f64 (sqrt.f64 (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))) 2))
✓	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

Compiler

Compiled 17490 to 5354 computations (69.4% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
✓	0.0b	(+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)
✓	6.1b	(/.f64 (*.f64 y t) (-.f64 a z))
✓	12.3b	(/.f64 (*.f64 t z) (-.f64 a z))

series232.0ms (2.6%)

Counts

4 → 144

Calls

4 calls:

94.0ms	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
57.0ms	(/.f64 (*.f64 y t) (-.f64 a z))
52.0ms	(+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)
29.0ms	(/.f64 (*.f64 t z) (-.f64 a z))

rewrite147.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

294×	`log1p-udef_binary64`
181×	`egg-rr`
160×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`

Counts

4 → 181

Calls

4 calls:

137.0ms	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
137.0ms	(+.f64 (/.f64 (*.f64 y t) (-.f64 a z)) x)
137.0ms	(/.f64 (*.f64 y t) (-.f64 a z))
137.0ms	(/.f64 (*.f64 t z) (-.f64 a z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	58
1	304	58
2	4710	58
3	5205	58
0	0	0
1	0	0

simplify196.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

678×	`fma-def_binary64`
629×	`times-frac_binary64`
546×	`fma-neg_binary64`
482×	`associate-/l*_binary64`
456×	`cancel-sign-sub-inv_binary64`

Counts

325 → 274

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	3767
1	450	3767
2	1466	3013
3	4596	3013
4	5027	3013

prune360.0ms (4.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	274	4	278

Error

Counts

278 → 4

Alt Table

Status	Error	Program
✓	2.6b	(+.f64 x (*.f64 t (/.f64 1 (/.f64 (-.f64 a z) (-.f64 y z)))))
✓	12.3b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	29.9b	(+.f64 x (pow.f64 (sqrt.f64 (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))) 2))
✓	2.8b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

Compiler

Compiled 7688 to 1770 computations (77% saved)

regimes2.3s (26.3%)

Accuracy

Total 0.2b remaining (92.6%)

Threshold costs 0.2b (92.6%)

Counts

131 → 3

Compiler

Compiled 16340 to 10488 computations (35.8% saved)

bsearch7.0ms (0.1%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify26.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

54×	`distribute-rgt-neg-in_binary64`
48×	`cancel-sign-sub-inv_binary64`
37×	`distribute-lft-neg-in_binary64`
35×	`neg-sub0_binary64`
35×	`neg-mul-1_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	97
1	51	97
2	75	95
3	107	93
4	134	93
5	152	93
6	165	93
7	185	93
8	211	93
9	249	93
10	285	93
11	306	93
12	310	93
13	306	93

end162.0ms (1.8%)

Compiler: Compiled 210 to 104 computations (50.5% saved)

Iter	Nodes	Cost
0	31	97
1	51	97
2	75	95
3	107	93
4	134	93
5	152	93
6	165	93
7	185	93
8	211	93
9	249	93
10	285	93
11	306	93
12	310	93
13	306	93

Iter	Nodes	Cost
0	31	97
1	51	97
2	75	95
3	107	93
4	134	93
5	152	93
6	165	93
7	185	93
8	211	93
9	249	93
10	285	93
11	306	93
12	310	93
13	306	93

Details

analyze1.4s (16.4%)

sample1.3s (14.4%)

simplify118.0ms (1.3%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series55.0ms (0.6%)

rewrite69.0ms (0.8%)

simplify92.0ms (1%)

prune90.0ms (1%)

localize9.0ms (0.1%)

series101.0ms (1.1%)

rewrite105.0ms (1.2%)

simplify124.0ms (1.4%)

prune604.0ms (6.9%)

localize16.0ms (0.2%)

series144.0ms (1.6%)

rewrite243.0ms (2.8%)

simplify194.0ms (2.2%)

prune645.0ms (7.3%)

localize20.0ms (0.2%)

series232.0ms (2.6%)

rewrite147.0ms (1.7%)

simplify196.0ms (2.2%)

prune360.0ms (4.1%)

regimes2.3s (26.3%)

bsearch7.0ms (0.1%)

simplify26.0ms (0.3%)

end162.0ms (1.8%)

Profiling

Iter	Nodes	Cost
0	31	97
1	51	97
2	75	95
3	107	93
4	134	93
5	152	93
6	165	93
7	185	93
8	211	93
9	249	93
10	285	93
11	306	93
12	310	93
13	306	93