Details

analyze1.3s (23.8%)

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)

sample1.1s (21.6%)

Results

989.0ms	8256×	body	128	valid
91.0ms	787×	body	128	invalid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify113.0ms (2.2%)

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 (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	11.6b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	2.2b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series44.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

31.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
13.0ms	(/.f64 t (-.f64 a z))

rewrite67.0ms (1.3%)

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 → 60

Calls

2 calls:

66.0ms	(/.f64 t (-.f64 a z))
66.0ms	(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

simplify88.0ms (1.7%)

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

144 → 116

Iterations

Useful iterations: 2 (0.0ms)

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

prune82.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	114	4	118

Error

0.0b

Counts

118 → 4

Alt Table

Status	Error	Program
	35.4b	(-.f64 (+.f64 (/.f64 (.f64 y (.f64 t z)) (pow.f64 a 2)) (+.f64 x (/.f64 (.f64 y t) a))) (/.f64 (.f64 t z) a))
▶	2.1b	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
✓	2.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	11.6b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 2459 to 788 computations (68% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series96.0ms (1.8%)

Counts

3 → 120

Calls

3 calls:

42.0ms	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
41.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
13.0ms	(/.f64 y (-.f64 a z))

rewrite83.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

276×	`expm1-udef_binary64`
276×	`log1p-udef_binary64`
150×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`
145×	`expm1-log1p-u_binary64`

Counts

3 → 96

Calls

3 calls:

81.0ms	(+.f64 x (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))))
81.0ms	(/.f64 y (-.f64 a z))
81.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	283	34
2	4326	34
3	5167	34
0	0	0
1	0	0

simplify107.0ms (2%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-def_binary64`
742×	`times-frac_binary64`
648×	`cancel-sign-sub-inv_binary64`
571×	`fma-neg_binary64`
276×	`sub-neg_binary64`

Counts

216 → 193

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	3879
1	511	3879
2	1844	3322
3	4384	3317
4	5050	3317

prune153.0ms (2.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	191	2	193
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	193	4	197

Error

Counts

197 → 4

Alt Table

Status	Error	Program
	31.5b	(+.f64 x (fma.f64 (/.f64 (.f64 t y) a) (/.f64 z a) (/.f64 (.f64 t (-.f64 y z)) a)))
▶	2.1b	(+.f64 x (.f64 t (-.f64 (.f64 y (/.f64 1 (-.f64 a z))) (/.f64 z (-.f64 a z)))))
✓	2.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	11.6b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 4940 to 1628 computations (67% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 t (-.f64 (.f64 y (/.f64 1 (-.f64 a z))) (/.f64 z (-.f64 a z)))))
✓	0.0b	(/.f64 1 (-.f64 a z))
✓	0.2b	(*.f64 y (/.f64 1 (-.f64 a z)))
✓	2.7b	(.f64 t (-.f64 (.f64 y (/.f64 1 (-.f64 a z))) (/.f64 z (-.f64 a z))))

series150.0ms (2.8%)

Counts

4 → 168

Calls

4 calls:

55.0ms	(.f64 t (-.f64 (.f64 y (/.f64 1 (-.f64 a z))) (/.f64 z (-.f64 a z))))
43.0ms	(+.f64 x (.f64 t (-.f64 (.f64 y (/.f64 1 (-.f64 a z))) (/.f64 z (-.f64 a z)))))
42.0ms	(*.f64 y (/.f64 1 (-.f64 a z)))
9.0ms	(/.f64 1 (-.f64 a z))

rewrite83.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

286×	`expm1-udef_binary64`
286×	`log1p-udef_binary64`
160×	`add-sqr-sqrt_binary64`
153×	`log1p-expm1-u_binary64`
153×	`expm1-log1p-u_binary64`

Counts

4 → 106

Calls

4 calls:

81.0ms	(+.f64 x (.f64 t (-.f64 (.f64 y (/.f64 1 (-.f64 a z))) (/.f64 z (-.f64 a z)))))
81.0ms	(/.f64 1 (-.f64 a z))
81.0ms	(*.f64 y (/.f64 1 (-.f64 a z)))
81.0ms	(.f64 t (-.f64 (.f64 y (/.f64 1 (-.f64 a z))) (/.f64 z (-.f64 a z))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	55
1	314	41
2	4266	41
3	5101	41
0	0	0
1	0	0

simplify146.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

760×	`times-frac_binary64`
759×	`fma-neg_binary64`
660×	`cancel-sign-sub-inv_binary64`
287×	`sub-neg_binary64`
172×	`associate-/r/_binary64`

Counts

274 → 217

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	211	4653
1	561	4635
2	2024	3988
3	4364	3972
4	4998	3972
5	4984	3972

prune126.0ms (2.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	217	4	221

Error

Counts

221 → 4

Alt Table

Status	Error	Program
	31.5b	(+.f64 x (fma.f64 (/.f64 (.f64 t y) a) (/.f64 z a) (/.f64 (.f64 t (-.f64 y z)) a)))
✓	2.1b	(+.f64 x (.f64 t (-.f64 (.f64 y (/.f64 1 (-.f64 a z))) (/.f64 z (-.f64 a z)))))
✓	2.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
▶	11.6b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 5443 to 1894 computations (65.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
✓	0.0b	(*.f64 (-.f64 y z) t)
✓	11.9b	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

series79.0ms (1.5%)

Counts

3 → 144

Calls

3 calls:

41.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
29.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
9.0ms	(*.f64 (-.f64 y z) t)

rewrite80.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

521×	`fma-def_binary64`
265×	`fma-neg_binary64`
248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`
135×	`add-sqr-sqrt_binary64`

Counts

3 → 133

Calls

3 calls:

77.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
77.0ms	(*.f64 (-.f64 y z) t)
77.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	254	36
2	3732	34
3	5282	34
0	0	0
1	0	0

simplify105.0ms (2%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-def_binary64`
603×	`times-frac_binary64`
562×	`fma-neg_binary64`
554×	`cancel-sign-sub-inv_binary64`
486×	`associate-/l*_binary64`

Counts

277 → 214

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	3870
1	429	3780
2	1545	2844
3	4536	2839
4	5026	2839

prune132.0ms (2.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	213	1	214
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	214	4	218

Error

Counts

218 → 4

Alt Table

Status	Error	Program
✓	2.1b	(+.f64 x (.f64 t (-.f64 (.f64 y (/.f64 1 (-.f64 a z))) (/.f64 z (-.f64 a z)))))
	11.7b	(+.f64 x (pow.f64 (/.f64 (-.f64 a z) (*.f64 (-.f64 y z) t)) -1))
✓	2.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	11.6b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 4638 to 1342 computations (71.1% saved)

regimes1.0s (19.6%)

Accuracy

Total 0.2b remaining (91.9%)

Threshold costs 0.2b (91.9%)

Counts

104 → 3

Compiler

Compiled 12427 to 7975 computations (35.8% saved)

bsearch3.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	80
1	29	80
2	34	80
3	36	80
4	37	80
5	36	80

end65.0ms (1.2%)

Compiler: Compiled 191 to 80 computations (58.1% saved)

Details

analyze1.3s (23.8%)

sample1.1s (21.6%)

simplify113.0ms (2.2%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series44.0ms (0.8%)

rewrite67.0ms (1.3%)

simplify88.0ms (1.7%)

prune82.0ms (1.6%)

localize8.0ms (0.2%)

series96.0ms (1.8%)

rewrite83.0ms (1.6%)

simplify107.0ms (2%)

prune153.0ms (2.9%)

localize11.0ms (0.2%)

series150.0ms (2.8%)

rewrite83.0ms (1.6%)

simplify146.0ms (2.8%)

prune126.0ms (2.4%)

localize7.0ms (0.1%)

series79.0ms (1.5%)

rewrite80.0ms (1.5%)

simplify105.0ms (2%)

prune132.0ms (2.5%)

regimes1.0s (19.6%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end65.0ms (1.2%)

Profiling