Details

analyze1.2s (29.3%)

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
13.3%	86.5%	0.2%	9
19.9%	79.9%	0.2%	10
24%	75.2%	0.8%	11
25.4%	72.7%	1.9%	12
35.8%	59.6%	4.6%	13
42%	52.3%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.3s (31.7%)

Results

942.0ms	8256×	body	128	valid
312.0ms	2120×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify46.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-def_binary64`
660×	`fma-neg_binary64`
203×	`cancel-sign-sub-inv_binary64`
145×	`distribute-rgt-in_binary64`
99×	`div-sub_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	30	11
3	64	11
4	150	11
5	309	11
6	545	11
7	995	11
8	1956	11
9	2893	11
10	3408	11
11	3457	11
12	3487	11
13	3492	11
14	3492	11

Stop Event

1×

saturated

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
▶	0.8b	(fma.f64 (-.f64 z x) (/.f64 y t) x)
	4.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.8b	(fma.f64 (-.f64 z x) (/.f64 y t) x)

series18.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

18.0ms

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

rewrite41.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

455×	`log-prod_binary64`
446×	`prod-diff_binary64`
197×	`fma-def_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	175	11
2	2476	11

Stop Event

1×	node limit

Counts

1 → 29

Calls

1 calls:

39.0ms

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

simplify71.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

752×	`fma-def_binary64`
737×	`fma-neg_binary64`
248×	`cancel-sign-sub-inv_binary64`
179×	`distribute-rgt-in_binary64`
131×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	777
1	71	561
2	166	552
3	387	480
4	832	480
5	1538	480
6	2608	480
7	3638	480
8	3678	480
9	3722	480
10	3780	480
11	3780	480

Stop Event

1×

saturated

Counts

77 → 42

prune23.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Error

0.0b

Counts

44 → 4

Alt Table

Status	Error	Program
	28.6b	(/.f64 (-.f64 (.f64 (.f64 (-.f64 z x) (/.f64 y t)) (.f64 (-.f64 z x) (/.f64 y t))) (.f64 x x)) (fma.f64 (-.f64 z x) (/.f64 y t) (neg.f64 x)))
	6.6b	(fma.f64 y (/.f64 (-.f64 z x) t) x)
✓	0.8b	(fma.f64 (-.f64 z x) (/.f64 y t) x)
▶	4.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

Compiler

Compiled 660 to 192 computations (70.9% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
✓	0.0b	(*.f64 y (-.f64 z x))
✓	4.4b	(/.f64 (*.f64 y (-.f64 z x)) t)

series49.0ms (1.2%)

Counts

3 → 104

Calls

3 calls:

20.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
18.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)
11.0ms	(*.f64 y (-.f64 z x))

rewrite63.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

367×	`fma-def_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
196×	`fma-neg_binary64`
173×	`log-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	205	30
2	3162	28

Stop Event

1×	node limit

Counts

3 → 132

Calls

3 calls:

60.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
60.0ms	(*.f64 y (-.f64 z x))
60.0ms	(/.f64 (*.f64 y (-.f64 z x)) t)

simplify91.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

949×	`fma-def_binary64`
753×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`
168×	`distribute-rgt-in_binary64`
125×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	1232
1	94	1016
2	220	1016
3	526	944
4	1127	944
5	2086	944
6	3282	944
7	3962	944
8	3989	944
9	4019	944
10	4024	944
11	4024	944

Stop Event

1×

saturated

Counts

236 → 153

prune97.0ms (2.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	149	4	153
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	151	6	157

Error

Counts

157 → 6

Alt Table

Status	Error	Program
✓	0.8b	(fma.f64 (-.f64 z x) (/.f64 y t) x)
	6.7b	(fma.f64 y (/.f64 1 (/.f64 t (-.f64 z x))) x)
	5.7b	(+.f64 x (pow.f64 (/.f64 (/.f64 t (-.f64 z x)) y) -1))
✓	4.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
	30.0b	(fma.f64 (/.f64 y (sqrt.f64 t)) (/.f64 (-.f64 z x) (sqrt.f64 t)) x)
▶	4.4b	(fma.f64 (*.f64 y (-.f64 z x)) (/.f64 1 t) x)

Compiler

Compiled 2333 to 690 computations (70.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (-.f64 z x))
✓	4.1b	(fma.f64 (*.f64 y (-.f64 z x)) (/.f64 1 t) x)

series18.0ms (0.4%)

Counts

1 → 48

Calls

1 calls:

18.0ms

(fma.f64 (*.f64 y (-.f64 z x)) (/.f64 1 t) x)

rewrite45.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

491×	`log-prod_binary64`
433×	`prod-diff_binary64`
207×	`fma-def_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	208	13
2	2683	13

Stop Event

1×	node limit

Counts

1 → 29

Calls

1 calls:

44.0ms

(fma.f64 (*.f64 y (-.f64 z x)) (/.f64 1 t) x)

simplify70.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

752×	`fma-def_binary64`
731×	`fma-neg_binary64`
248×	`cancel-sign-sub-inv_binary64`
179×	`distribute-rgt-in_binary64`
131×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	777
1	71	561
2	166	552
3	388	480
4	833	480
5	1539	480
6	2599	480
7	3626	480
8	3666	480
9	3710	480
10	3768	480
11	3768	480

Stop Event

1×

saturated

Counts

77 → 42

prune42.0ms (1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	70	6	76

Error

Counts

76 → 6

Alt Table

Status	Error	Program
✓	0.8b	(fma.f64 (-.f64 z x) (/.f64 y t) x)
	6.7b	(fma.f64 y (/.f64 1 (/.f64 t (-.f64 z x))) x)
▶	5.7b	(+.f64 x (pow.f64 (/.f64 (/.f64 t (-.f64 z x)) y) -1))
✓	4.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
	30.0b	(fma.f64 (/.f64 y (sqrt.f64 t)) (/.f64 (-.f64 z x) (sqrt.f64 t)) x)
✓	4.4b	(fma.f64 (*.f64 y (-.f64 z x)) (/.f64 1 t) x)

Compiler

Compiled 1067 to 371 computations (65.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 z x))
✓	0.0b	(+.f64 x (pow.f64 (/.f64 (/.f64 t (-.f64 z x)) y) -1))
✓	0.5b	(pow.f64 (/.f64 (/.f64 t (-.f64 z x)) y) -1)
✓	6.4b	(/.f64 (/.f64 t (-.f64 z x)) y)

series266.0ms (6.4%)

Counts

4 → 168

Calls

4 calls:

117.0ms	(pow.f64 (/.f64 (/.f64 t (-.f64 z x)) y) -1)
102.0ms	(+.f64 x (pow.f64 (/.f64 (/.f64 t (-.f64 z x)) y) -1))
33.0ms	(/.f64 (/.f64 t (-.f64 z x)) y)
14.0ms	(/.f64 t (-.f64 z x))

rewrite70.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

352×	`fma-def_binary64`
235×	`expm1-udef_binary64`
235×	`log1p-udef_binary64`
198×	`fma-neg_binary64`
186×	`egg-rr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	46
1	253	40
2	3822	38

Stop Event

1×	node limit

Counts

4 → 186

Calls

4 calls:

67.0ms	(/.f64 t (-.f64 z x))
67.0ms	(+.f64 x (pow.f64 (/.f64 (/.f64 t (-.f64 z x)) y) -1))
67.0ms	(pow.f64 (/.f64 (/.f64 t (-.f64 z x)) y) -1)
67.0ms	(/.f64 (/.f64 t (-.f64 z x)) y)

simplify96.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

945×	`fma-neg_binary64`
476×	`times-frac_binary64`
447×	`associate-/l*_binary64`
350×	`fma-def_binary64`
299×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	102	2868
1	303	2562
2	1024	2391
3	4752	2391

Stop Event

1×	node limit

Counts

354 → 236

prune168.0ms (4.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	2	0	2
Picked	1	0	1
Done	0	3	3
Total	238	4	242

Error

Counts

242 → 4

Alt Table

Status	Error	Program
	5.7b	(+.f64 x (/.f64 y (/.f64 t (-.f64 z x))))
✓	4.3b	(+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))
✓	0.8b	(fma.f64 (-.f64 z x) (/.f64 y t) x)
✓	4.4b	(fma.f64 (*.f64 y (-.f64 z x)) (/.f64 1 t) x)

Compiler

Compiled 3965 to 1428 computations (64% saved)

regimes239.0ms (5.8%)

Accuracy

Total 2.0b remaining (99%)

Threshold costs 0b (0%)

Counts

38 → 1

Compiler

Compiled 2531 to 1598 computations (36.9% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	15	11
3	17	11
4	18	11

Stop Event

1×

saturated

end58.0ms (1.4%)

Compiler: Compiled 76 to 46 computations (39.5% saved)

Details

analyze1.2s (29.3%)

sample1.3s (31.7%)

simplify46.0ms (1.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series18.0ms (0.4%)

rewrite41.0ms (1%)

simplify71.0ms (1.7%)

prune23.0ms (0.6%)

localize6.0ms (0.1%)

series49.0ms (1.2%)

rewrite63.0ms (1.5%)

simplify91.0ms (2.2%)

prune97.0ms (2.4%)

localize6.0ms (0.2%)

series18.0ms (0.4%)

rewrite45.0ms (1.1%)

simplify70.0ms (1.7%)

prune42.0ms (1%)

localize9.0ms (0.2%)

series266.0ms (6.4%)

rewrite70.0ms (1.7%)

simplify96.0ms (2.3%)

prune168.0ms (4.1%)

regimes239.0ms (5.8%)

simplify9.0ms (0.2%)

end58.0ms (1.4%)

Profiling