Details

analyze394.0ms (12.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
34.3%	62.4%	3.3%	9
42.1%	49.9%	7.9%	10
53.8%	37.8%	8.3%	11
56.2%	33%	10.9%	12
60.3%	25.6%	14.1%	13
66.4%	19.4%	14.2%	14

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample939.0ms (29.1%)

Results

757.0ms	8256×	body	128	valid
67.0ms	725×	body	128	invalid

Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify32.0ms (1%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
419×	`fma-neg_binary64`
208×	`distribute-rgt-in_binary64`
163×	`distribute-lft-in_binary64`
138×	`unsub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	20	13
2	49	11
3	153	11
4	470	11
5	1119	11
6	1863	11
7	2564	11
8	2672	11
9	2672	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
	3.6b	(fma.f64 z (-.f64 (*.f64 x y) x) x)
▶	3.6b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

Compiler

Compiled 66 to 42 computations (36.4% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 y) z)
✓	3.4b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

series14.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))
5.0ms	(*.f64 (-.f64 1 y) z)

rewrite46.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

555×	`prod-diff_binary64`
479×	`log-prod_binary64`
199×	`fma-def_binary64`
175×	`expm1-udef_binary64`
173×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	195	20
2	2550	20

Stop Event

1×	node limit

Counts

2 → 69

Calls

2 calls:

45.0ms	(*.f64 (-.f64 1 y) z)
45.0ms	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

simplify48.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

613×	`fma-neg_binary64`
436×	`fma-def_binary64`
126×	`unsub-neg_binary64`
117×	`distribute-rgt-in_binary64`
102×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	508
1	71	448
2	184	448
3	411	448
4	847	448
5	1662	448
6	2273	448
7	2429	448
8	2441	448
9	2441	448

Stop Event

1×

saturated

Counts

117 → 85

prune58.0ms (1.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	83	4	87

Error

0.0b

Counts

87 → 4

Alt Table

Status	Error	Program
	22.1b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 (-.f64 1 y) z) 3)) x) (fma.f64 (*.f64 (-.f64 1 y) z) (fma.f64 (-.f64 1 y) z 1) 1))
	3.6b	(fma.f64 z (-.f64 (*.f64 x y) x) x)
▶	1.7b	(fma.f64 (*.f64 z x) (+.f64 y -1) x)
✓	3.6b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

Compiler

Compiled 1217 to 775 computations (36.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.7b	(fma.f64 (*.f64 z x) (+.f64 y -1) x)

series9.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(fma.f64 (*.f64 z x) (+.f64 y -1) x)

rewrite38.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

785×	`log1p-expm1-u_binary64`
785×	`expm1-log1p-u_binary64`
146×	`prod-diff_binary64`
84×	`add-sqr-sqrt_binary64`
78×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	164	11
2	2049	11

Stop Event

1×	node limit

Counts

1 → 23

Calls

1 calls:

37.0ms

(fma.f64 (*.f64 z x) (+.f64 y -1) x)

simplify43.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

839×	`fma-def_binary64`
458×	`fma-neg_binary64`
142×	`distribute-rgt-in_binary64`
135×	`unsub-neg_binary64`
110×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	462
1	74	372
2	189	372
3	497	372
4	1277	372
5	2190	372
6	2772	372
7	2792	372
8	2792	372

Stop Event

1×

saturated

Counts

59 → 36

prune23.0ms (0.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	36	4	40

Error

0.0b

Counts

40 → 4

Alt Table

Status	Error	Program
	22.1b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 (-.f64 1 y) z) 3)) x) (fma.f64 (*.f64 (-.f64 1 y) z) (fma.f64 (-.f64 1 y) z 1) 1))
▶	3.6b	(fma.f64 z (-.f64 (*.f64 x y) x) x)
✓	1.7b	(fma.f64 (*.f64 z x) (+.f64 y -1) x)
✓	3.6b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

Compiler

Compiled 522 to 286 computations (45.2% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 x y) x)
✓	3.4b	(fma.f64 z (-.f64 (*.f64 x y) x) x)

series14.0ms (0.4%)

Counts

2 → 60

Calls

2 calls:

9.0ms	(fma.f64 z (-.f64 (*.f64 x y) x) x)
5.0ms	(-.f64 (*.f64 x y) x)

rewrite49.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

778×	`log1p-expm1-u_binary64`
778×	`expm1-log1p-u_binary64`
680×	`prod-diff_binary64`
115×	`egg-rr`
79×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	151	18
2	2051	18

Stop Event

1×	node limit

Counts

2 → 115

Calls

2 calls:

47.0ms	(-.f64 (*.f64 x y) x)
47.0ms	(fma.f64 z (-.f64 (*.f64 x y) x) x)

simplify54.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
436×	`fma-neg_binary64`
144×	`distribute-rgt-in_binary64`
133×	`unsub-neg_binary64`
112×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	620
1	90	530
2	218	530
3	554	530
4	1345	530
5	2164	530
6	2657	530
7	2677	530
8	2677	530

Stop Event

1×

saturated

Counts

175 → 136

prune75.0ms (2.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	136	4	140

Error

0.0b

Counts

140 → 4

Alt Table

Status	Error	Program
▶	22.1b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 (-.f64 1 y) z) 3)) x) (fma.f64 (*.f64 (-.f64 1 y) z) (fma.f64 (-.f64 1 y) z 1) 1))
✓	3.6b	(fma.f64 z (-.f64 (*.f64 x y) x) x)
✓	1.7b	(fma.f64 (*.f64 z x) (+.f64 y -1) x)
✓	3.6b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

Compiler

Compiled 2233 to 717 computations (67.9% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (*.f64 (-.f64 1 y) z) (fma.f64 (-.f64 1 y) z 1) 1)
✓	0.2b	(pow.f64 (*.f64 (-.f64 1 y) z) 3)
✓	3.1b	(.f64 (-.f64 1 (pow.f64 (.f64 (-.f64 1 y) z) 3)) x)
✓	18.3b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 (-.f64 1 y) z) 3)) x) (fma.f64 (*.f64 (-.f64 1 y) z) (fma.f64 (-.f64 1 y) z 1) 1))

series470.0ms (14.6%)

Counts

4 → 120

Calls

4 calls:

359.0ms	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 (-.f64 1 y) z) 3)) x) (fma.f64 (*.f64 (-.f64 1 y) z) (fma.f64 (-.f64 1 y) z 1) 1))
89.0ms	(.f64 (-.f64 1 (pow.f64 (.f64 (-.f64 1 y) z) 3)) x)
12.0ms	(pow.f64 (*.f64 (-.f64 1 y) z) 3)
10.0ms	(fma.f64 (*.f64 (-.f64 1 y) z) (fma.f64 (-.f64 1 y) z 1) 1)

rewrite71.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

592×	`prod-diff_binary64`
151×	`add-sqr-sqrt_binary64`
144×	`add-cbrt-cube_binary64`
144×	`log1p-expm1-u_binary64`
144×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	80
1	308	80
2	4088	80

Stop Event

1×	node limit

Counts

4 → 115

Calls

4 calls:

68.0ms	(fma.f64 (*.f64 (-.f64 1 y) z) (fma.f64 (-.f64 1 y) z 1) 1)
68.0ms	(pow.f64 (*.f64 (-.f64 1 y) z) 3)
68.0ms	(.f64 (-.f64 1 (pow.f64 (.f64 (-.f64 1 y) z) 3)) x)
68.0ms	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 (-.f64 1 y) z) 3)) x) (fma.f64 (*.f64 (-.f64 1 y) z) (fma.f64 (-.f64 1 y) z 1) 1))

simplify98.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

378×	`times-frac_binary64`
368×	`associate-/l*_binary64`
360×	`fma-def_binary64`
317×	`associate-r_binary64`
275×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	369	8863
1	1365	7797

Stop Event

1×	node limit

Counts

235 → 190

prune218.0ms (6.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	189	5	194

Error

Counts

194 → 5

Alt Table

Status	Error	Program
	42.8b	(.f64 (/.f64 z (+.f64 1 (.f64 y (-.f64 y 2)))) (.f64 x (-.f64 (fma.f64 3 y (pow.f64 y 3)) (fma.f64 3 (.f64 y y) 1))))
✓	22.1b	(/.f64 (.f64 (-.f64 1 (pow.f64 (.f64 (-.f64 1 y) z) 3)) x) (fma.f64 (*.f64 (-.f64 1 y) z) (fma.f64 (-.f64 1 y) z 1) 1))
✓	3.6b	(fma.f64 z (-.f64 (*.f64 x y) x) x)
✓	1.7b	(fma.f64 (*.f64 z x) (+.f64 y -1) x)
✓	3.6b	(.f64 x (-.f64 1 (.f64 (-.f64 1 y) z)))

Compiler

Compiled 9968 to 7005 computations (29.7% saved)

regimes398.0ms (12.4%)

Accuracy

Total 0.5b remaining (97.5%)

Threshold costs 0.5b (97.5%)

Counts

28 → 3

Compiler

Compiled 2950 to 2073 computations (29.7% saved)

bsearch1.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	57
1	42	57
2	61	57
3	78	57
4	103	57
5	133	57
6	166	57
7	195	57
8	223	57
9	267	57
10	332	57
11	385	57
12	412	57
13	416	57

Stop Event

1×

saturated

end91.0ms (2.8%)

Compiler: Compiled 174 to 119 computations (31.6% saved)

Iter	Nodes	Cost
0	22	57
1	42	57
2	61	57
3	78	57
4	103	57
5	133	57
6	166	57
7	195	57
8	223	57
9	267	57
10	332	57
11	385	57
12	412	57
13	416	57

Iter	Nodes	Cost
0	22	57
1	42	57
2	61	57
3	78	57
4	103	57
5	133	57
6	166	57
7	195	57
8	223	57
9	267	57
10	332	57
11	385	57
12	412	57
13	416	57

Details

analyze394.0ms (12.2%)

sample939.0ms (29.1%)

simplify32.0ms (1%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series14.0ms (0.4%)

rewrite46.0ms (1.4%)

simplify48.0ms (1.5%)

prune58.0ms (1.8%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite38.0ms (1.2%)

simplify43.0ms (1.3%)

prune23.0ms (0.7%)

localize5.0ms (0.2%)

series14.0ms (0.4%)

rewrite49.0ms (1.5%)

simplify54.0ms (1.7%)

prune75.0ms (2.3%)

localize12.0ms (0.4%)

series470.0ms (14.6%)

rewrite71.0ms (2.2%)

simplify98.0ms (3.1%)

prune218.0ms (6.7%)

regimes398.0ms (12.4%)

bsearch1.0ms (0%)

simplify11.0ms (0.3%)

end91.0ms (2.8%)

Profiling

Iter	Nodes	Cost
0	22	57
1	42	57
2	61	57
3	78	57
4	103	57
5	133	57
6	166	57
7	195	57
8	223	57
9	267	57
10	332	57
11	385	57
12	412	57
13	416	57