Details

analyze1.3s (21%)

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)

sample1.5s (24.4%)

Results

1.3s	8254×	body	128	valid
123.0ms	706×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify117.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1894×	`fma-neg_binary64`
843×	`div-sub_binary64`
750×	`fma-def_binary64`
582×	`times-frac_binary64`
397×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	37	14
3	78	14
4	163	14
5	295	14
6	645	14
7	1554	14
8	3040	14
9	3228	14
10	3469	14
11	3370	14
12	3363	14
13	3398	14
14	4949	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
▶	1.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	9.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

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 (-.f64 z t) (-.f64 a t))
✓	1.7b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series51.0ms (0.9%)

Counts

2 → 96

Calls

2 calls:

35.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
16.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite70.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

365×	`fma-def_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
200×	`fma-neg_binary64`
192×	`log-pow_binary64`

Counts

2 → 79

Calls

2 calls:

59.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
59.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	226	24
2	3220	24
3	5187	24
0	0	0
1	0	0

simplify131.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
678×	`cancel-sign-sub-inv_binary64`
618×	`times-frac_binary64`
513×	`fma-neg_binary64`
322×	`sub-neg_binary64`

Counts

175 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	172	2919
1	524	2907
2	1879	2271
3	4349	2257
4	5031	2257

prune125.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	150	4	154
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	151	5	156

Error

0.0b

Counts

156 → 5

Alt Table

Status	Error	Program
	31.5b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) 2)
	3.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
▶	1.8b	(fma.f64 y (fma.f64 z (/.f64 1 (-.f64 a t)) (neg.f64 (/.f64 t (-.f64 a t)))) x)
✓	1.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Compiler

Compiled 3524 to 1188 computations (66.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.0b	(/.f64 t (-.f64 a t))
✓	0.1b	(fma.f64 z (/.f64 1 (-.f64 a t)) (neg.f64 (/.f64 t (-.f64 a t))))
✓	1.7b	(fma.f64 y (fma.f64 z (/.f64 1 (-.f64 a t)) (neg.f64 (/.f64 t (-.f64 a t)))) x)

series83.0ms (1.4%)

Counts

4 → 144

Calls

4 calls:

46.0ms	(fma.f64 y (fma.f64 z (/.f64 1 (-.f64 a t)) (neg.f64 (/.f64 t (-.f64 a t)))) x)
22.0ms	(fma.f64 z (/.f64 1 (-.f64 a t)) (neg.f64 (/.f64 t (-.f64 a t))))
9.0ms	(/.f64 t (-.f64 a t))
7.0ms	(/.f64 1 (-.f64 a t))

rewrite209.0ms (3.5%)

Algorithm

2×	batch-egg-rewrite

Rules

793×	`prod-diff_binary64`
459×	`egg-rr`
230×	`log1p-udef_binary64`
138×	`add-sqr-sqrt_binary64`
128×	`log1p-expm1-u_binary64`

Counts

4 → 459

Calls

4 calls:

190.0ms	(/.f64 1 (-.f64 a t))
190.0ms	(/.f64 t (-.f64 a t))
190.0ms	(fma.f64 z (/.f64 1 (-.f64 a t)) (neg.f64 (/.f64 t (-.f64 a t))))
190.0ms	(fma.f64 y (fma.f64 z (/.f64 1 (-.f64 a t)) (neg.f64 (/.f64 t (-.f64 a t)))) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	56
1	273	50
2	3211	50
3	5177	50
0	0	0
1	0	0

simplify120.0ms (2%)

Algorithm

1×	egg-herbie

Rules

682×	`cancel-sign-sub-inv_binary64`
658×	`fma-neg_binary64`
634×	`times-frac_binary64`
339×	`sub-neg_binary64`
178×	`+-commutative_binary64`

Counts

603 → 561

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	200	3864
1	600	3816
2	2137	3109
3	4411	3086
4	4977	3086

prune416.0ms (6.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	561	0	561
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	561	5	566

Error

0.0b

Counts

566 → 5

Alt Table

Status	Error	Program
	31.5b	(pow.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) 2)
▶	3.9b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	9.8b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))
✓	1.8b	(fma.f64 y (fma.f64 z (/.f64 1 (-.f64 a t)) (neg.f64 (/.f64 t (-.f64 a t)))) x)
✓	1.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Compiler

Compiled 22885 to 6791 computations (70.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	0.0b	(/.f64 y (-.f64 a t))
✓	10.8b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series85.0ms (1.4%)

Counts

3 → 132

Calls

3 calls:

41.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
27.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
17.0ms	(/.f64 y (-.f64 a t))

rewrite75.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

539×	`fma-def_binary64`
258×	`fma-neg_binary64`
248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`
136×	`egg-rr`

Counts

3 → 136

Calls

3 calls:

72.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
72.0ms	(/.f64 y (-.f64 a t))
72.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
1	254	34
2	3702	34
3	5260	34
0	0	0
1	0	0

simplify123.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-neg_binary64`
652×	`times-frac_binary64`
560×	`associate-/l*_binary64`
381×	`sub-neg_binary64`
222×	`associate--l+_binary64`

Counts

268 → 234

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	3939
1	608	3612
2	2177	3113
3	4943	3113
4	5559	3113

prune172.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	232	2	234
Fresh	2	0	2
Picked	1	0	1
Done	0	2	2
Total	235	4	239

Error

Counts

239 → 4

Alt Table

Status	Error	Program
✓	1.8b	(fma.f64 y (fma.f64 z (/.f64 1 (-.f64 a t)) (neg.f64 (/.f64 t (-.f64 a t)))) x)
✓	1.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	3.8b	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
▶	1.7b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))

Compiler

Compiled 5311 to 1674 computations (68.5% saved)

localize9.0ms (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))))
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	2.0b	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))

series89.0ms (1.5%)

Counts

3 → 144

Calls

3 calls:

43.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
29.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))
16.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

rewrite80.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

294×	`fma-neg_binary64`
258×	`expm1-udef_binary64`
258×	`log1p-udef_binary64`
141×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`

Counts

3 → 134

Calls

3 calls:

76.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
76.0ms	(/.f64 (-.f64 a t) (-.f64 z t))
76.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	263	37
2	4054	37
3	5166	37
0	0	0
1	0	0

simplify88.0ms (1.5%)

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`

Counts

278 → 244

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	234	4417
1	702	4081
2	2637	3498
3	5005	3498

prune151.0ms (2.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	244	0	244
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	244	4	248

Error

Counts

248 → 4

Alt Table

Status	Error	Program
✓	1.8b	(fma.f64 y (fma.f64 z (/.f64 1 (-.f64 a t)) (neg.f64 (/.f64 t (-.f64 a t)))) x)
✓	1.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	3.8b	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
✓	1.7b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))

Compiler

Compiled 5756 to 1910 computations (66.8% saved)

regimes965.0ms (16.1%)

Accuracy

Total 0.6b remaining (97.5%)

Threshold costs 0.6b (97.5%)

Counts

106 → 3

Compiler

Compiled 12140 to 7793 computations (35.8% saved)

bsearch3.0ms (0%)

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
7×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	91
1	44	91
2	54	91
3	65	91
4	71	91
5	74	91
6	75	91
7	74	91

end72.0ms (1.2%)

Compiler: Compiled 202 to 93 computations (54% saved)

Details

analyze1.3s (21%)

sample1.5s (24.4%)

simplify117.0ms (2%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series51.0ms (0.9%)

rewrite70.0ms (1.2%)

simplify131.0ms (2.2%)

prune125.0ms (2.1%)

localize10.0ms (0.2%)

series83.0ms (1.4%)

rewrite209.0ms (3.5%)

simplify120.0ms (2%)

prune416.0ms (6.9%)

localize9.0ms (0.2%)

series85.0ms (1.4%)

rewrite75.0ms (1.3%)

simplify123.0ms (2.1%)

prune172.0ms (2.9%)

localize9.0ms (0.2%)

series89.0ms (1.5%)

rewrite80.0ms (1.3%)

simplify88.0ms (1.5%)

prune151.0ms (2.5%)

regimes965.0ms (16.1%)

bsearch3.0ms (0%)

simplify8.0ms (0.1%)

end72.0ms (1.2%)

Profiling