Details

analyze1.3s (27.6%)

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
22.4%	77.4%	0.2%	13
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (24.8%)

Results

1.0s	8254×	body	128	valid
97.0ms	781×	body	128	invalid
0.0ms	1×	body	512	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify22.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

611×	`times-frac_binary64`
577×	`div-sub_binary64`
529×	`fma-neg_binary64`
259×	`fma-def_binary64`
192×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	21	14
2	41	14
3	82	14
4	188	14
5	381	14
6	902	14
7	2369	14

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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
▶	0.6b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
	1.6b	(fma.f64 (-.f64 t z) (/.f64 y (-.f64 t a)) x)

Compiler

Compiled 88 to 52 computations (40.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	0.8b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

series90.0ms (1.9%)

Counts

3 → 144

Calls

3 calls:

42.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
28.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
17.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite71.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

280×	`fma-neg_binary64`
252×	`expm1-udef_binary64`
252×	`log1p-udef_binary64`
137×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	257	37
2	4024	37

Stop Event

1×	node limit

Counts

3 → 110

Calls

3 calls:

69.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
69.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
69.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

simplify78.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

627×	`times-frac_binary64`
520×	`sub-neg_binary64`
290×	`associate--l+_binary64`
214×	`associate--r+_binary64`
206×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	4417
1	767	4078
2	2702	3496

Stop Event

1×	node limit

Counts

254 → 222

prune204.0ms (4.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	217	5	222
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	218	6	224

Error

0.0b

Counts

224 → 6

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
	9.4b	(+.f64 x (-.f64 (/.f64 (.f64 y z) (-.f64 a t)) (/.f64 (.f64 y t) (-.f64 a t))))
	0.6b	(+.f64 x (.f64 y (.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))))
▶	0.6b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
	9.4b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
	9.4b	(+.f64 x (/.f64 1 (/.f64 (-.f64 a t) (*.f64 y (-.f64 z t)))))

Compiler

Compiled 5460 to 1950 computations (64.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
✓	0.1b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	0.9b	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))

series92.0ms (2%)

Counts

3 → 144

Calls

3 calls:

45.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
30.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))
17.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

rewrite70.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

258×	`expm1-udef_binary64`
258×	`log1p-udef_binary64`
141×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`
136×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	263	37
2	4303	37

Stop Event

1×	node limit

Counts

3 → 118

Calls

3 calls:

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

simplify75.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

805×	`times-frac_binary64`
532×	`sub-neg_binary64`
296×	`associate--l+_binary64`
215×	`associate--r+_binary64`
209×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	4417
1	793	4081
2	2853	3769

Stop Event

1×	node limit

Counts

262 → 230

prune186.0ms (3.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	228	2	230
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	229	7	236

Error

Counts

236 → 7

Alt Table

Status	Error	Program
✓	0.6b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
	35.1b	(+.f64 x (*.f64 (/.f64 (sqrt.f64 y) (-.f64 a t)) (/.f64 (sqrt.f64 y) (/.f64 1 (-.f64 z t)))))
✓	0.6b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
▶	1.6b	(fma.f64 (/.f64 y (-.f64 a t)) (-.f64 z t) x)
	9.4b	(+.f64 x (-.f64 (/.f64 (.f64 y z) (-.f64 a t)) (/.f64 (.f64 y t) (-.f64 a t))))
	9.4b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))
	9.4b	(+.f64 x (/.f64 1 (/.f64 (-.f64 a t) (*.f64 y (-.f64 z t)))))

Compiler

Compiled 5686 to 1991 computations (65% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.6b	(fma.f64 (/.f64 y (-.f64 a t)) (-.f64 z t) x)

series32.0ms (0.7%)

Counts

1 → 60

Calls

1 calls:

32.0ms

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

rewrite52.0ms (1.1%)

Algorithm

1×	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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	223	14
2	3237	14

Stop Event

1×	node limit

Counts

1 → 23

Calls

1 calls:

51.0ms

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

simplify37.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

686×	`associate--l+_binary64`
471×	`times-frac_binary64`
468×	`fma-def_binary64`
426×	`associate-/l*_binary64`
366×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	106	1832
1	329	1832
2	1261	1328

Stop Event

1×	node limit

Counts

83 → 65

prune52.0ms (1.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	66	6	72

Error

Counts

72 → 6

Alt Table

Status	Error	Program
▶	1.7b	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
✓	0.6b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
✓	1.6b	(fma.f64 (/.f64 y (-.f64 a t)) (-.f64 z t) x)
	9.4b	(+.f64 x (-.f64 (/.f64 (.f64 y z) (-.f64 a t)) (/.f64 (.f64 y t) (-.f64 a t))))
	35.1b	(+.f64 x (*.f64 (/.f64 (sqrt.f64 y) (-.f64 a t)) (/.f64 (sqrt.f64 y) (/.f64 1 (-.f64 z t)))))
	9.4b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 1595 to 519 computations (67.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
✓	0.0b	(/.f64 (-.f64 a t) y)
✓	8.8b	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))

series80.0ms (1.7%)

Counts

3 → 136

Calls

3 calls:

42.0ms	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
29.0ms	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))
9.0ms	(/.f64 (-.f64 a t) y)

rewrite67.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

262×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`
143×	`add-sqr-sqrt_binary64`
138×	`log1p-expm1-u_binary64`
138×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	266	34
2	4452	34

Stop Event

1×	node limit

Counts

3 → 118

Calls

3 calls:

65.0ms	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
65.0ms	(/.f64 (-.f64 a t) y)
65.0ms	(/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y))

simplify67.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

990×	`cancel-sign-sub-inv_binary64`
902×	`fma-def_binary64`
521×	`times-frac_binary64`
374×	`sub-neg_binary64`
222×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	3786
1	620	3198
2	2110	2956

Stop Event

1×	node limit

Counts

254 → 204

prune150.0ms (3.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	204	6	210

Error

Counts

210 → 6

Alt Table

Status	Error	Program
✓	1.7b	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
✓	0.6b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
✓	1.6b	(fma.f64 (/.f64 y (-.f64 a t)) (-.f64 z t) x)
	34.0b	(+.f64 x (/.f64 (-.f64 z t) (pow.f64 (sqrt.f64 (/.f64 (-.f64 a t) y)) 2)))
	9.4b	(+.f64 x (-.f64 (/.f64 (.f64 y z) (-.f64 a t)) (/.f64 (.f64 y t) (-.f64 a t))))
	9.4b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 4672 to 1459 computations (68.8% saved)

regimes726.0ms (15.3%)

Accuracy

Total 1.4b remaining (99.4%)

Threshold costs 0b (0%)

Counts

97 → 1

Compiler

Compiled 12621 to 8137 computations (35.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	24	22
2	29	22
3	32	22
4	33	22

Stop Event

1×

saturated

end73.0ms (1.5%)

Compiler: Compiled 144 to 86 computations (40.3% saved)

Details

analyze1.3s (27.6%)

sample1.2s (24.8%)

simplify22.0ms (0.5%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series90.0ms (1.9%)

rewrite71.0ms (1.5%)

simplify78.0ms (1.6%)

prune204.0ms (4.3%)

localize7.0ms (0.2%)

series92.0ms (2%)

rewrite70.0ms (1.5%)

simplify75.0ms (1.6%)

prune186.0ms (3.9%)

localize7.0ms (0.2%)

series32.0ms (0.7%)

rewrite52.0ms (1.1%)

simplify37.0ms (0.8%)

prune52.0ms (1.1%)

localize7.0ms (0.2%)

series80.0ms (1.7%)

rewrite67.0ms (1.4%)

simplify67.0ms (1.4%)

prune150.0ms (3.2%)

regimes726.0ms (15.3%)

simplify3.0ms (0.1%)

end73.0ms (1.5%)

Profiling