Details

analyze887.0ms (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
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
23.4%	74.9%	1.8%	11
27.3%	69%	3.7%	12
36.6%	56.5%	6.8%	13
40.5%	52%	7.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (28.6%)

Symmetry

(sort y t)

Results

875.0ms	8256×	body	128	valid
214.0ms	1906×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify30.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

992×	`fma-def_binary64`
302×	`fma-neg_binary64`
112×	`distribute-rgt-in_binary64`
87×	`associate-l_binary64`
82×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	20	10
2	47	10
3	111	10
4	229	10
5	343	10
6	552	10
7	911	10
8	1666	10
9	2363	10
10	2418	10
11	2424	10
12	2424	10

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	10.1b	(.f64 y (.f64 t (-.f64 x z)))
▶	6.9b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

Compiler

Compiled 68 to 41 computations (39.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(-.f64 (.f64 x y) (.f64 z y))
✓	6.5b	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)

series23.0ms (0.5%)

Counts

2 → 84

Calls

2 calls:

16.0ms	(.f64 (-.f64 (.f64 x y) (*.f64 z y)) t)
7.0ms	(-.f64 (.f64 x y) (.f64 z y))

rewrite66.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

557×	`log-prod_binary64`
498×	`fma-def_binary64`
260×	`egg-rr`
216×	`fma-neg_binary64`
186×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	201	17
2	2783	17

Stop Event

1×	node limit

Counts

2 → 260

Calls

2 calls:

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

simplify56.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-def_binary64`
312×	`fma-neg_binary64`
100×	`distribute-rgt-in_binary64`
83×	`associate-r_binary64`
81×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	708
1	80	708
2	199	708
3	443	708
4	829	708
5	1298	708
6	1823	708
7	2221	708
8	2223	708
9	2223	708

Stop Event

1×

saturated

Counts

344 → 275

prune163.0ms (3.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	269	6	275
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	270	7	277

Error

0.0b

Counts

277 → 7

Alt Table

Status	Error	Program
	6.8b	(fma.f64 (.f64 y (-.f64 x z)) t (.f64 (fma.f64 y (neg.f64 z) (*.f64 y z)) t))
▶	5.1b	(.f64 (-.f64 x z) (.f64 y t))
	41.7b	(/.f64 (.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 y z) 3)) t) (fma.f64 (.f64 y z) (.f64 y (+.f64 x z)) (pow.f64 (.f64 x y) 2)))
	6.9b	(fma.f64 t (.f64 x y) (.f64 t (*.f64 y (neg.f64 z))))
	7.3b	(.f64 (fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) y) (*.f64 y (neg.f64 z))) t)
	10.1b	(.f64 y (.f64 t (-.f64 x z)))
	35.8b	(pow.f64 (sqrt.f64 (.f64 y (.f64 (-.f64 x z) t))) 2)

Compiler

Compiled 5378 to 1289 computations (76% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	5.0b	(.f64 (-.f64 x z) (.f64 y t))

series13.0ms (0.3%)

Counts

1 → 32

Calls

1 calls:

13.0ms

(*.f64 (-.f64 x z) (*.f64 y t))

rewrite42.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

870×	`log1p-expm1-u_binary64`
870×	`expm1-log1p-u_binary64`
359×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
83×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	170	10
2	2303	10

Stop Event

1×	node limit

Counts

1 → 21

Calls

1 calls:

42.0ms

(*.f64 (-.f64 x z) (*.f64 y t))

simplify42.0ms (1%)

Algorithm

1×	egg-herbie

Rules

922×	`fma-def_binary64`
400×	`fma-neg_binary64`
146×	`cancel-sign-sub-inv_binary64`
88×	`distribute-rgt-in_binary64`
75×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	308
1	52	308
2	123	308
3	215	308
4	328	308
5	554	308
6	947	308
7	1511	308
8	2215	308
9	2429	308
10	2443	308
11	2443	308

Stop Event

1×

saturated

Counts

53 → 28

prune21.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	28	7	35

Error

0.0b

Counts

35 → 7

Alt Table

Status	Error	Program
▶	6.8b	(fma.f64 (.f64 y (-.f64 x z)) t (.f64 (fma.f64 y (neg.f64 z) (*.f64 y z)) t))
✓	5.1b	(.f64 (-.f64 x z) (.f64 y t))
	41.7b	(/.f64 (.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 y z) 3)) t) (fma.f64 (.f64 y z) (.f64 y (+.f64 x z)) (pow.f64 (.f64 x y) 2)))
	6.9b	(fma.f64 t (.f64 x y) (.f64 t (*.f64 y (neg.f64 z))))
	7.3b	(.f64 (fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) y) (*.f64 y (neg.f64 z))) t)
	10.1b	(.f64 y (.f64 t (-.f64 x z)))
	30.4b	(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 z z)) (.f64 y t)) (+.f64 x z))

Compiler

Compiled 548 to 246 computations (55.1% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 x z))
✓	6.5b	(fma.f64 (.f64 y (-.f64 x z)) t (.f64 (fma.f64 y (neg.f64 z) (*.f64 y z)) t))
✓	50.7b	(fma.f64 y (neg.f64 z) (*.f64 y z))

series36.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

21.0ms	(fma.f64 (.f64 y (-.f64 x z)) t (.f64 (fma.f64 y (neg.f64 z) (*.f64 y z)) t))
9.0ms	(fma.f64 y (neg.f64 z) (*.f64 y z))
6.0ms	(*.f64 y (-.f64 x z))

rewrite51.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

607×	`log-prod_binary64`
255×	`fma-def_binary64`
214×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`
193×	`log-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	252	33
2	3424	31

Stop Event

1×	node limit

Counts

3 → 89

Calls

3 calls:

49.0ms	(*.f64 y (-.f64 x z))
49.0ms	(fma.f64 (.f64 y (-.f64 x z)) t (.f64 (fma.f64 y (neg.f64 z) (*.f64 y z)) t))
49.0ms	(fma.f64 y (neg.f64 z) (*.f64 y z))

simplify59.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

858×	`fma-def_binary64`
292×	`fma-neg_binary64`
121×	`cancel-sign-sub-inv_binary64`
98×	`unsub-neg_binary64`
95×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	732
1	87	732
2	227	732
3	533	732
4	975	732
5	1568	732
6	2110	732
7	2430	732
8	2434	732
9	2434	732

Stop Event

1×

saturated

Counts

197 → 107

prune58.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	107	7	114

Error

0.0b

Counts

114 → 7

Alt Table

Status	Error	Program
✓	6.8b	(fma.f64 (.f64 y (-.f64 x z)) t (.f64 (fma.f64 y (neg.f64 z) (*.f64 y z)) t))
✓	5.1b	(.f64 (-.f64 x z) (.f64 y t))
	41.7b	(/.f64 (.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 y z) 3)) t) (fma.f64 (.f64 y z) (.f64 y (+.f64 x z)) (pow.f64 (.f64 x y) 2)))
▶	6.9b	(fma.f64 t (.f64 x y) (.f64 t (*.f64 y (neg.f64 z))))
	7.3b	(.f64 (fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) y) (*.f64 y (neg.f64 z))) t)
	10.1b	(.f64 y (.f64 t (-.f64 x z)))
	30.4b	(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 z z)) (.f64 y t)) (+.f64 x z))

Compiler

Compiled 2242 to 570 computations (74.6% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.2b	(fma.f64 t (.f64 x y) (.f64 t (*.f64 y (neg.f64 z))))
✓	7.6b	(.f64 t (.f64 y (neg.f64 z)))

series28.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

19.0ms	(fma.f64 t (.f64 x y) (.f64 t (*.f64 y (neg.f64 z))))
9.0ms	(.f64 t (.f64 y (neg.f64 z)))

rewrite43.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

848×	`log1p-expm1-u_binary64`
848×	`expm1-log1p-u_binary64`
308×	`prod-diff_binary64`
114×	`associate-r_binary64`
105×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	204	20
2	2640	20

Stop Event

1×	node limit

Counts

2 → 40

Calls

2 calls:

43.0ms	(fma.f64 t (.f64 x y) (.f64 t (*.f64 y (neg.f64 z))))
43.0ms	(.f64 t (.f64 y (neg.f64 z)))

simplify57.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

810×	`fma-def_binary64`
291×	`fma-neg_binary64`
120×	`cancel-sign-sub-inv_binary64`
94×	`unsub-neg_binary64`
92×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	792
1	80	792
2	220	792
3	515	792
4	962	792
5	1535	792
6	2053	792
7	2379	792
8	2383	792
9	2383	792

Stop Event

1×

saturated

Counts

124 → 49

prune27.0ms (0.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	49	7	56

Error

0.0b

Counts

56 → 7

Alt Table

Status	Error	Program
✓	6.8b	(fma.f64 (.f64 y (-.f64 x z)) t (.f64 (fma.f64 y (neg.f64 z) (*.f64 y z)) t))
✓	5.1b	(.f64 (-.f64 x z) (.f64 y t))
	41.7b	(/.f64 (.f64 (-.f64 (pow.f64 (.f64 x y) 3) (pow.f64 (.f64 y z) 3)) t) (fma.f64 (.f64 y z) (.f64 y (+.f64 x z)) (pow.f64 (.f64 x y) 2)))
✓	6.9b	(fma.f64 t (.f64 x y) (.f64 t (*.f64 y (neg.f64 z))))
	7.3b	(.f64 (fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) y) (*.f64 y (neg.f64 z))) t)
	10.1b	(.f64 y (.f64 t (-.f64 x z)))
	30.4b	(/.f64 (.f64 (-.f64 (.f64 x x) (.f64 z z)) (.f64 y t)) (+.f64 x z))

Compiler

Compiled 792 to 248 computations (68.7% saved)

regimes996.0ms (23.6%)

Accuracy

Total 0.3b remaining (92.9%)

Threshold costs 0.3b (92.9%)

Counts

66 → 5

Compiler

Compiled 5884 to 3764 computations (36% saved)

bsearch2.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	139
1	56	139
2	76	139
3	85	139
4	90	139
5	91	139

Stop Event

1×

saturated

end274.0ms (6.5%)

Compiler: Compiled 523 to 199 computations (62% saved)

Details

analyze887.0ms (21%)

sample1.2s (28.6%)

simplify30.0ms (0.7%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series23.0ms (0.5%)

rewrite66.0ms (1.6%)

simplify56.0ms (1.3%)

prune163.0ms (3.9%)

localize5.0ms (0.1%)

series13.0ms (0.3%)

rewrite42.0ms (1%)

simplify42.0ms (1%)

prune21.0ms (0.5%)

localize10.0ms (0.2%)

series36.0ms (0.8%)

rewrite51.0ms (1.2%)

simplify59.0ms (1.4%)

prune58.0ms (1.4%)

localize8.0ms (0.2%)

series28.0ms (0.7%)

rewrite43.0ms (1%)

simplify57.0ms (1.4%)

prune27.0ms (0.6%)

regimes996.0ms (23.6%)

bsearch2.0ms (0%)

simplify6.0ms (0.1%)

end274.0ms (6.5%)

Profiling