Details

analyze797.0ms (11.8%)

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
1.6%	98.2%	0.2%	8
19.1%	80.7%	0.2%	9
22%	77.8%	0.2%	10
34.5%	65.3%	0.2%	11
44.2%	55.7%	0.2%	12
53.3%	45.5%	1.2%	13
55.8%	42.7%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.5s (21.9%)

Results

1.4s	8256×	body	128	valid
79.0ms	663×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify20.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

609×	`times-frac_binary64`
569×	`div-sub_binary64`
535×	`fma-def_binary64`
336×	`fma-neg_binary64`
186×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	18	13
2	30	13
3	68	13
4	167	13
5	324	13
6	712	13
7	2100	13

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

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
	8.7b	(*.f64 (-.f64 y x) (/.f64 t (-.f64 y z)))
▶	1.7b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 74 to 44 computations (40.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	1.7b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series48.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

30.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
16.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

rewrite113.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

952×	`prod-diff_binary64`
258×	`egg-rr`
111×	`add-sqr-sqrt_binary64`
106×	`log1p-expm1-u_binary64`
106×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	208	23
2	3214	23

Stop Event

1×	node limit

Counts

2 → 258

Calls

2 calls:

103.0ms	(/.f64 (-.f64 x y) (-.f64 z y))
103.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
665×	`times-frac_binary64`
419×	`cancel-sign-sub-inv_binary64`
327×	`sub-neg_binary64`
161×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	150	2783
1	469	2777
2	1799	2157

Stop Event

1×	node limit

Counts

342 → 328

prune255.0ms (3.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	323	5	328
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	324	6	330

Error

Counts

330 → 6

Alt Table

Status	Error	Program
	8.7b	(*.f64 (-.f64 y x) (/.f64 t (-.f64 y z)))
▶	1.8b	(.f64 (+.f64 (fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (.f64 (/.f64 y (-.f64 z y)) 1))) (fma.f64 (neg.f64 (/.f64 y (-.f64 z y))) 1 (*.f64 (/.f64 y (-.f64 z y)) 1))) t)
	2.1b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))
	2.2b	(.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (-.f64 z y)) (neg.f64 (.f64 (/.f64 1 (-.f64 z y)) y))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 z y))) y (*.f64 (/.f64 1 (-.f64 z y)) y))) t)
	13.3b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
	40.5b	(/.f64 (/.f64 (*.f64 (-.f64 x y) t) (sqrt.f64 (-.f64 z y))) (sqrt.f64 (-.f64 z y)))

Compiler

Compiled 14578 to 4215 computations (71.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series102.0ms (1.5%)

Counts

4 → 132

Calls

4 calls:

63.0ms	(.f64 (+.f64 (fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (.f64 (/.f64 y (-.f64 z y)) 1))) (fma.f64 (neg.f64 (/.f64 y (-.f64 z y))) 1 (*.f64 (/.f64 y (-.f64 z y)) 1))) t)
25.0ms	(fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (*.f64 (/.f64 y (-.f64 z y)) 1)))
7.0ms	(/.f64 y (-.f64 z y))
6.0ms	(/.f64 1 (-.f64 z y))

rewrite69.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

258×	`expm1-udef_binary64`
258×	`log1p-udef_binary64`
156×	`add-sqr-sqrt_binary64`
147×	`add-cbrt-cube_binary64`
147×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	75
1	355	61
2	4391	61

Stop Event

1×	node limit

Counts

4 → 131

Calls

4 calls:

66.0ms	(/.f64 y (-.f64 z y))
66.0ms	(/.f64 1 (-.f64 z y))
66.0ms	(fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (*.f64 (/.f64 y (-.f64 z y)) 1)))
66.0ms	(.f64 (+.f64 (fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (.f64 (/.f64 y (-.f64 z y)) 1))) (fma.f64 (neg.f64 (/.f64 y (-.f64 z y))) 1 (*.f64 (/.f64 y (-.f64 z y)) 1))) t)

simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
680×	`times-frac_binary64`
429×	`cancel-sign-sub-inv_binary64`
343×	`sub-neg_binary64`
177×	`fma-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	177	3695
1	539	3659
2	2070	3336

Stop Event

1×	node limit

Counts

263 → 232

prune313.0ms (4.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	374	0	374
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	374	6	380

Error

Counts

380 → 6

Alt Table

Status	Error	Program
	8.7b	(*.f64 (-.f64 y x) (/.f64 t (-.f64 y z)))
✓	1.8b	(.f64 (+.f64 (fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (.f64 (/.f64 y (-.f64 z y)) 1))) (fma.f64 (neg.f64 (/.f64 y (-.f64 z y))) 1 (*.f64 (/.f64 y (-.f64 z y)) 1))) t)
▶	2.1b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))
	2.2b	(.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (-.f64 z y)) (neg.f64 (.f64 (/.f64 1 (-.f64 z y)) y))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 z y))) y (*.f64 (/.f64 1 (-.f64 z y)) y))) t)
	13.3b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
	40.5b	(/.f64 (/.f64 (*.f64 (-.f64 x y) t) (sqrt.f64 (-.f64 z y))) (sqrt.f64 (-.f64 z y)))

Compiler

Compiled 14303 to 5580 computations (61% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z y) (-.f64 x y))
✓	2.1b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))

series45.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

28.0ms	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))
17.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

rewrite115.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

979×	`prod-diff_binary64`
278×	`egg-rr`
115×	`add-sqr-sqrt_binary64`
110×	`log1p-expm1-u_binary64`
110×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	214	23
2	3470	23

Stop Event

1×	node limit

Counts

2 → 278

Calls

2 calls:

102.0ms	(/.f64 (-.f64 z y) (-.f64 x y))
102.0ms	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))

simplify56.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

826×	`times-frac_binary64`
776×	`fma-def_binary64`
447×	`cancel-sign-sub-inv_binary64`
341×	`sub-neg_binary64`
141×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	2603
1	511	2498
2	1941	2262

Stop Event

1×	node limit

Counts

362 → 348

prune271.0ms (4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	345	3	348
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	348	6	354

Error

Counts

354 → 6

Alt Table

Status	Error	Program
✓	2.1b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))
▶	2.2b	(/.f64 t (+.f64 (fma.f64 z (/.f64 1 (-.f64 x y)) (neg.f64 (.f64 (/.f64 1 (-.f64 x y)) y))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x y))) y (.f64 (/.f64 1 (-.f64 x y)) y))))
	8.7b	(+.f64 (.f64 x (/.f64 t (-.f64 z y))) (.f64 (neg.f64 y) (/.f64 t (-.f64 z y))))
✓	1.8b	(.f64 (+.f64 (fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (.f64 (/.f64 y (-.f64 z y)) 1))) (fma.f64 (neg.f64 (/.f64 y (-.f64 z y))) 1 (*.f64 (/.f64 y (-.f64 z y)) 1))) t)
	31.2b	(pow.f64 (sqrt.f64 (*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))) 2)
	13.3b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))

Compiler

Compiled 14964 to 4059 computations (72.9% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (/.f64 1 (-.f64 x y)) (neg.f64 (*.f64 (/.f64 1 (-.f64 x y)) y)))
✓	0.2b	(*.f64 (/.f64 1 (-.f64 x y)) y)
✓	2.1b	(/.f64 t (+.f64 (fma.f64 z (/.f64 1 (-.f64 x y)) (neg.f64 (.f64 (/.f64 1 (-.f64 x y)) y))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x y))) y (.f64 (/.f64 1 (-.f64 x y)) y))))
✓	55.0b	(fma.f64 (neg.f64 (/.f64 1 (-.f64 x y))) y (*.f64 (/.f64 1 (-.f64 x y)) y))

series373.0ms (5.5%)

Counts

4 → 132

Calls

4 calls:

249.0ms	(fma.f64 (neg.f64 (/.f64 1 (-.f64 x y))) y (*.f64 (/.f64 1 (-.f64 x y)) y))
96.0ms	(/.f64 t (+.f64 (fma.f64 z (/.f64 1 (-.f64 x y)) (neg.f64 (.f64 (/.f64 1 (-.f64 x y)) y))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x y))) y (.f64 (/.f64 1 (-.f64 x y)) y))))
21.0ms	(fma.f64 z (/.f64 1 (-.f64 x y)) (neg.f64 (*.f64 (/.f64 1 (-.f64 x y)) y)))
7.0ms	(*.f64 (/.f64 1 (-.f64 x y)) y)

rewrite66.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

266×	`log1p-udef_binary64`
166×	`add-sqr-sqrt_binary64`
156×	`add-cbrt-cube_binary64`
156×	`log1p-expm1-u_binary64`
156×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	84
1	331	64
2	4721	64

Stop Event

1×	node limit

Counts

4 → 118

Calls

4 calls:

63.0ms	(fma.f64 z (/.f64 1 (-.f64 x y)) (neg.f64 (*.f64 (/.f64 1 (-.f64 x y)) y)))
63.0ms	(*.f64 (/.f64 1 (-.f64 x y)) y)
63.0ms	(/.f64 t (+.f64 (fma.f64 z (/.f64 1 (-.f64 x y)) (neg.f64 (.f64 (/.f64 1 (-.f64 x y)) y))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x y))) y (.f64 (/.f64 1 (-.f64 x y)) y))))
63.0ms	(fma.f64 (neg.f64 (/.f64 1 (-.f64 x y))) y (*.f64 (/.f64 1 (-.f64 x y)) y))

simplify60.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

823×	`times-frac_binary64`
563×	`associate-/l*_binary64`
430×	`associate-/r*_binary64`
193×	`associate-l_binary64`
142×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	365	5035
1	1352	4899

Stop Event

1×	node limit

Counts

250 → 220

prune277.0ms (4.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	265	0	265
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	265	6	271

Error

Counts

271 → 6

Alt Table

Status	Error	Program
✓	2.1b	(/.f64 t (/.f64 (-.f64 z y) (-.f64 x y)))
✓	2.2b	(/.f64 t (+.f64 (fma.f64 z (/.f64 1 (-.f64 x y)) (neg.f64 (.f64 (/.f64 1 (-.f64 x y)) y))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x y))) y (.f64 (/.f64 1 (-.f64 x y)) y))))
	8.7b	(+.f64 (.f64 x (/.f64 t (-.f64 z y))) (.f64 (neg.f64 y) (/.f64 t (-.f64 z y))))
✓	1.8b	(.f64 (+.f64 (fma.f64 x (/.f64 1 (-.f64 z y)) (neg.f64 (.f64 (/.f64 y (-.f64 z y)) 1))) (fma.f64 (neg.f64 (/.f64 y (-.f64 z y))) 1 (*.f64 (/.f64 y (-.f64 z y)) 1))) t)
	31.2b	(pow.f64 (sqrt.f64 (*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))) 2)
	13.3b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))

Compiler

Compiled 11456 to 5078 computations (55.7% saved)

regimes2.0s (29.9%)

Accuracy

Total 1.3b remaining (98.9%)

Threshold costs 0b (0%)

Counts

249 → 3

Compiler

Compiled 34857 to 20158 computations (42.2% saved)

bsearch8.0ms (0.1%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	86
1	43	84
2	58	84
3	70	84
4	77	84
5	80	84
6	81	84

Stop Event

1×

saturated

end90.0ms (1.3%)

Compiler: Compiled 264 to 123 computations (53.4% saved)

Details

analyze797.0ms (11.8%)

sample1.5s (21.9%)

simplify20.0ms (0.3%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series48.0ms (0.7%)

rewrite113.0ms (1.7%)

simplify55.0ms (0.8%)

prune255.0ms (3.8%)

localize14.0ms (0.2%)

series102.0ms (1.5%)

rewrite69.0ms (1%)

simplify64.0ms (1%)

prune313.0ms (4.6%)

localize6.0ms (0.1%)

series45.0ms (0.7%)

rewrite115.0ms (1.7%)

simplify56.0ms (0.8%)

prune271.0ms (4%)

localize17.0ms (0.3%)

series373.0ms (5.5%)

rewrite66.0ms (1%)

simplify60.0ms (0.9%)

prune277.0ms (4.1%)

regimes2.0s (29.9%)

bsearch8.0ms (0.1%)

simplify5.0ms (0.1%)

end90.0ms (1.3%)

Profiling