Details

analyze994.0ms (20.9%)

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
12.5%	85.6%	1.9%	11
19.5%	76.8%	3.7%	12
25.7%	64.7%	9.6%	13
31.6%	54.7%	13.7%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.1s (23.9%)

Results

848.0ms	8256×	body	128	valid
273.0ms	2543×	body	128	invalid

Compiler

Compiled 28 to 18 computations (35.7% saved)

preprocess38.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

832×	`unsub-neg_binary64`
388×	`+-commutative_binary64`
286×	`fma-def_binary64`
263×	`distribute-rgt-in_binary64`
262×	`associate-+l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	91
1	56	77
2	162	77
3	612	77
4	2556	77
5	4215	77
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify29.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
536×	`unsub-neg_binary64`
313×	`distribute-rgt-in_binary64`
251×	`sub-neg_binary64`
228×	`associate-+l+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	11
2	37	11
3	117	11
4	453	11
5	1476	11
6	2927	11
7	4018	11

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)

Compiler

Compiled 45 to 23 computations (48.9% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.2%)

Counts

1 → 48

Calls

12 calls:

1.0ms	(fma.f64 (-.f64 y z) (-.f64 t x) x)	x	-inf
1.0ms	(fma.f64 (-.f64 y z) (-.f64 t x) x)	t	-inf
1.0ms	(fma.f64 (-.f64 y z) (-.f64 t x) x)	y	-inf
1.0ms	(fma.f64 (-.f64 y z) (-.f64 t x) x)	x	inf
1.0ms	(fma.f64 (-.f64 y z) (-.f64 t x) x)	y	inf

rewrite40.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

782×	`prod-diff_binary64`
341×	`fma-def_binary64`
176×	`expm1-udef_binary64`
176×	`log1p-udef_binary64`
165×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	180	11
2	2584	11

Stop Event

1×	node limit

Counts

1 → 23

simplify98.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

2435×	`fma-neg_binary64`
504×	`fma-def_binary64`
312×	`sub-neg_binary64`
310×	`unsub-neg_binary64`
252×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 11 (0.0ms)

Iter	Nodes	Cost
0	41	788
1	131	783
2	362	783
3	885	701
4	2282	557
5	3827	557
6	4450	557
7	4526	557
8	4527	557
9	4527	557
10	4527	557
11	4527	485

Stop Event

1×	node limit

Counts

71 → 42

prune23.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	2	43

Error

0.0b

Counts

43 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
▶	0.0b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))

Compiler

Compiled 532 to 148 computations (72.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series39.0ms (0.8%)

Counts

4 → 87

Calls

42 calls:

3.0ms	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))	y	-inf
2.0ms	(+.f64 (.f64 y x) (.f64 t z))	x	-inf
2.0ms	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))	x	-inf
2.0ms	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))	y	inf
1.0ms	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))	x	inf

rewrite87.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

294×	`log1p-udef_binary64`
184×	`egg-rr`
160×	`add-sqr-sqrt_binary64`
156×	`log1p-expm1-u_binary64`
156×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	309	41
2	4990	41

Stop Event

1×	node limit

Counts

4 → 184

simplify50.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-neg_binary64`
485×	`fma-def_binary64`
300×	`unsub-neg_binary64`
271×	`sub-neg_binary64`
261×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	778
1	121	773
2	332	773
3	831	727
4	2107	655
5	4457	655

Stop Event

1×	node limit

Counts

271 → 216

prune161.0ms (3.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	214	2	216
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	214	4	218

Error

Counts

218 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
▶	17.1b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (.f64 (-.f64 (pow.f64 (.f64 y x) 2) (pow.f64 (.f64 t z) 2)) (/.f64 1 (-.f64 (.f64 y x) (*.f64 t z)))))
✓	0.0b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
	32.7b	(fma.f64 (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (neg.f64 (fma.f64 t z (*.f64 y x))))

Compiler

Compiled 5261 to 1157 computations (78% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (*.f64 y x) 2)
✓	0.3b	(/.f64 1 (-.f64 (.f64 y x) (.f64 t z)))
✓	0.5b	(-.f64 (pow.f64 (.f64 y x) 2) (pow.f64 (.f64 t z) 2))
✓	23.2b	(.f64 (-.f64 (pow.f64 (.f64 y x) 2) (pow.f64 (.f64 t z) 2)) (/.f64 1 (-.f64 (.f64 y x) (*.f64 t z))))

series150.0ms (3.2%)

Counts

4 → 168

Calls

42 calls:

25.0ms	(-.f64 (pow.f64 (.f64 y x) 2) (pow.f64 (.f64 t z) 2))	x	0
17.0ms	(/.f64 1 (-.f64 (.f64 y x) (.f64 t z)))	y	inf
6.0ms	(.f64 (-.f64 (pow.f64 (.f64 y x) 2) (pow.f64 (.f64 t z) 2)) (/.f64 1 (-.f64 (.f64 y x) (*.f64 t z))))	t	-inf
5.0ms	(.f64 (-.f64 (pow.f64 (.f64 y x) 2) (pow.f64 (.f64 t z) 2)) (/.f64 1 (-.f64 (.f64 y x) (*.f64 t z))))	y	inf
4.0ms	(.f64 (-.f64 (pow.f64 (.f64 y x) 2) (pow.f64 (.f64 t z) 2)) (/.f64 1 (-.f64 (.f64 y x) (*.f64 t z))))	y	0

rewrite73.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

275×	`log1p-udef_binary64`
160×	`add-sqr-sqrt_binary64`
160×	`log1p-expm1-u_binary64`
160×	`expm1-log1p-u_binary64`
157×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	64
1	341	44
2	4551	44

Stop Event

1×	node limit

Counts

4 → 142

simplify83.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

762×	`associate-/l*_binary64`
493×	`associate-/r*_binary64`
253×	`associate-r_binary64`
249×	`associate-l_binary64`
173×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	56	3384
1	198	3276
2	843	3180

Stop Event

1×	node limit

Counts

310 → 164

prune127.0ms (2.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	164	4	168

Error

Counts

168 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
✓	17.1b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (.f64 (-.f64 (pow.f64 (.f64 y x) 2) (pow.f64 (.f64 t z) 2)) (/.f64 1 (-.f64 (.f64 y x) (*.f64 t z)))))
✓	0.0b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
▶	32.7b	(fma.f64 (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (neg.f64 (fma.f64 t z (*.f64 y x))))

Compiler

Compiled 6143 to 2083 computations (66.1% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y t (fma.f64 z x x))
✓	0.0b	(sqrt.f64 (fma.f64 y t (fma.f64 z x x)))
✓	0.2b	(fma.f64 (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (neg.f64 (fma.f64 t z (*.f64 y x))))

series770.0ms (16.2%)

Counts

3 → 88

Calls

36 calls:

438.0ms	(fma.f64 (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (neg.f64 (fma.f64 t z (*.f64 y x))))	x	0
40.0ms	(fma.f64 (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (neg.f64 (fma.f64 t z (*.f64 y x))))	y	0
37.0ms	(fma.f64 (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (neg.f64 (fma.f64 t z (*.f64 y x))))	z	0
36.0ms	(fma.f64 (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (neg.f64 (fma.f64 t z (*.f64 y x))))	t	0
26.0ms	(fma.f64 (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (neg.f64 (fma.f64 t z (*.f64 y x))))	x	inf

rewrite73.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

487×	`prod-diff_binary64`
209×	`fma-def_binary64`
204×	`expm1-udef_binary64`
204×	`log1p-udef_binary64`
190×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	41
1	243	39
2	3012	39

Stop Event

1×	node limit

Counts

3 → 140

simplify43.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-def_binary64`
379×	`*-commutative_binary64`
330×	`cancel-sign-sub-inv_binary64`
290×	`associate-+l+_binary64`
241×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	1621
1	416	1595
2	1481	1501

Stop Event

1×	node limit

Counts

228 → 190

prune159.0ms (3.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	284	0	284
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	284	4	288

Error

Counts

288 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 (-.f64 y z) (-.f64 t x) x)
✓	17.1b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (.f64 (-.f64 (pow.f64 (.f64 y x) 2) (pow.f64 (.f64 t z) 2)) (/.f64 1 (-.f64 (.f64 y x) (*.f64 t z)))))
✓	0.0b	(-.f64 (+.f64 (.f64 y t) (+.f64 (.f64 z x) x)) (+.f64 (.f64 y x) (.f64 t z)))
✓	32.7b	(fma.f64 (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (sqrt.f64 (fma.f64 y t (fma.f64 z x x))) (neg.f64 (fma.f64 t z (*.f64 y x))))

Compiler

Compiled 10765 to 2450 computations (77.2% saved)

regimes450.0ms (9.5%)

Accuracy

Total 0.0b remaining (69.5%)

Threshold costs 0.0b (69.5%)

Counts

81 → 1

Compiler

Compiled 8984 to 5089 computations (43.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	13	19
2	18	19
3	20	19
4	21	19

Stop Event

1×

saturated

end65.0ms (1.4%)

Stop Event

1×

done

Compiler

Compiled 132 to 68 computations (48.5% saved)

Details

analyze994.0ms (20.9%)

sample1.1s (23.9%)

preprocess38.0ms (0.8%)

simplify29.0ms (0.6%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

series11.0ms (0.2%)

rewrite40.0ms (0.8%)

simplify98.0ms (2.1%)

prune23.0ms (0.5%)

localize10.0ms (0.2%)

series39.0ms (0.8%)

rewrite87.0ms (1.8%)

simplify50.0ms (1.1%)

prune161.0ms (3.4%)

localize16.0ms (0.3%)

series150.0ms (3.2%)

rewrite73.0ms (1.5%)

simplify83.0ms (1.8%)

prune127.0ms (2.7%)

localize14.0ms (0.3%)

series770.0ms (16.2%)

rewrite73.0ms (1.5%)

simplify43.0ms (0.9%)

prune159.0ms (3.3%)

regimes450.0ms (9.5%)

simplify2.0ms (0.1%)

end65.0ms (1.4%)

Profiling