Details

analyze372.0ms (5.2%)

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
18.7%	81.1%	0.1%	6
40.6%	59.3%	0.1%	7
45.2%	54.6%	0.1%	8
65.5%	34.3%	0.1%	9
78%	21.8%	0.1%	10
80%	19.5%	0.5%	11
81.7%	17.7%	0.5%	12
87.9%	11.3%	0.8%	13
88.3%	10.1%	1.6%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample1.8s (24.6%)

Results

1.5s	8256×	body	128	valid
44.0ms	246×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify104.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

649×	`fma-neg_binary64`
504×	`div-sub_binary64`
481×	`fma-def_binary64`
326×	`times-frac_binary64`
174×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	21	10
3	37	10
4	64	10
5	113	10
6	216	10
7	415	10
8	754	10
9	1183	10
10	1537	10
11	1612	10
12	1657	10
13	1684	10
14	1694	10
15	1702	10
16	1702	10
17	1600	10

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 30 to 18 computations (40% saved)

localize13.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series38.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

37.0ms

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

rewrite177.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

952×	`prod-diff_binary64`
728×	`fma-udef_binary64`
226×	`fma-neg_binary64`
166×	`expm1-udef_binary64`
166×	`log1p-udef_binary64`

Counts

1 → 68

Calls

1 calls:

173.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	167	10
2	2530	10
3	4730	10
4	4517	10
5	5108	10
0	0	0
1	0	0

simplify107.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

753×	`sub-neg_binary64`
431×	`associate--l+_binary64`
342×	`fma-def_binary64`
338×	`associate--r+_binary64`
311×	`associate-+l+_binary64`

Counts

104 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1081
1	225	1075
2	827	933
3	4185	927
4	4904	927
5	5012	927

prune160.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	3	101

Error

Counts

101 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
▶	0.1b	(+.f64 (+.f64 (/.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)))
	0.8b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x y)) 2) (pow.f64 (cbrt.f64 (-.f64 z y)) 2)) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))))

Compiler

Compiled 2390 to 838 computations (64.9% saved)

localize31.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 z y))
✓	0.0b	(+.f64 (/.f64 x (-.f64 z y)) (neg.f64 (*.f64 (/.f64 1 (-.f64 z y)) y)))
✓	0.2b	(*.f64 (/.f64 1 (-.f64 z y)) y)
✓	54.4b	(fma.f64 (neg.f64 (/.f64 1 (-.f64 z y))) y (*.f64 (/.f64 1 (-.f64 z y)) y))

series693.0ms (9.7%)

Counts

4 → 108

Calls

4 calls:

612.0ms	(fma.f64 (neg.f64 (/.f64 1 (-.f64 z y))) y (*.f64 (/.f64 1 (-.f64 z y)) y))
50.0ms	(+.f64 (/.f64 x (-.f64 z y)) (neg.f64 (*.f64 (/.f64 1 (-.f64 z y)) y)))
16.0ms	(*.f64 (/.f64 1 (-.f64 z y)) y)
14.0ms	(/.f64 1 (-.f64 z y))

rewrite170.0ms (2.4%)

Algorithm

2×	batch-egg-rewrite

Rules

444×	`fma-def_binary64`
342×	`fma-neg_binary64`
227×	`egg-rr`
220×	`expm1-udef_binary64`
220×	`log1p-udef_binary64`

Counts

4 → 227

Calls

4 calls:

161.0ms	(/.f64 1 (-.f64 z y))
161.0ms	(+.f64 (/.f64 x (-.f64 z y)) (neg.f64 (*.f64 (/.f64 1 (-.f64 z y)) y)))
161.0ms	(*.f64 (/.f64 1 (-.f64 z y)) y)
161.0ms	(fma.f64 (neg.f64 (/.f64 1 (-.f64 z y))) y (*.f64 (/.f64 1 (-.f64 z y)) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	47
1	289	34
2	3379	34
3	4934	34
0	0	0
1	0	0

simplify129.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

441×	`associate--l+_binary64`
425×	`fma-def_binary64`
391×	`associate--r+_binary64`
374×	`associate-+l+_binary64`
250×	`times-frac_binary64`

Counts

335 → 287

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	2051
1	294	2015
2	1080	1761
3	4997	1761

prune762.0ms (10.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	436	0	436
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	436	3	439

Error

Counts

439 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	0.1b	(+.f64 (+.f64 (/.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)))
▶	0.8b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x y)) 2) (pow.f64 (cbrt.f64 (-.f64 z y)) 2)) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))))

Compiler

Compiled 15550 to 6549 computations (57.9% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (cbrt.f64 (-.f64 x y)) 2)
✓	0.5b	(cbrt.f64 (-.f64 x y))
✓	0.6b	(cbrt.f64 (-.f64 z y))
✓	1.5b	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))

series684.0ms (9.5%)

Counts

4 → 108

Calls

4 calls:

441.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))
100.0ms	(pow.f64 (cbrt.f64 (-.f64 x y)) 2)
90.0ms	(cbrt.f64 (-.f64 x y))
51.0ms	(cbrt.f64 (-.f64 z y))

rewrite138.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

968×	`prod-diff_binary64`
129×	`add-sqr-sqrt_binary64`
124×	`log1p-expm1-u_binary64`
124×	`expm1-log1p-u_binary64`
122×	`add-cube-cbrt_binary64`

Counts

4 → 107

Calls

4 calls:

132.0ms	(pow.f64 (cbrt.f64 (-.f64 x y)) 2)
132.0ms	(cbrt.f64 (-.f64 x y))
132.0ms	(cbrt.f64 (-.f64 z y))
132.0ms	(cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	33
1	260	31
2	3383	31
3	5252	31
0	0	0
1	0	0

simplify250.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

738×	`times-frac_binary64`
661×	`fma-def_binary64`
286×	`*-commutative_binary64`
160×	`sqr-pow_binary64`
155×	`cancel-sign-sub-inv_binary64`

Counts

215 → 262

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	720	7417
1	2511	7247
2	5159	7247

prune578.0ms (8.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	262	0	262
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	262	3	265

Error

Counts

265 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	0.1b	(+.f64 (+.f64 (/.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)))
✓	0.8b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 x y)) 2) (pow.f64 (cbrt.f64 (-.f64 z y)) 2)) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))))

Compiler

Compiled 14095 to 7675 computations (45.5% saved)

regimes838.0ms (11.7%)

Accuracy

Total 0.0b remaining (60.2%)

Threshold costs 0.0b (60.2%)

Counts

101 → 1

Compiler

Compiled 9708 to 5586 computations (42.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`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	7	10
1	10	10
2	16	10
3	18	10
4	19	10
5	19	10

end126.0ms (1.8%)

Compiler: Compiled 88 to 51 computations (42% saved)

Details

analyze372.0ms (5.2%)

sample1.8s (24.6%)

simplify104.0ms (1.5%)

prune5.0ms (0.1%)

localize13.0ms (0.2%)

series38.0ms (0.5%)

rewrite177.0ms (2.5%)

simplify107.0ms (1.5%)

prune160.0ms (2.2%)

localize31.0ms (0.4%)

series693.0ms (9.7%)

rewrite170.0ms (2.4%)

simplify129.0ms (1.8%)

prune762.0ms (10.6%)

localize26.0ms (0.4%)

series684.0ms (9.5%)

rewrite138.0ms (1.9%)

simplify250.0ms (3.5%)

prune578.0ms (8.1%)

regimes838.0ms (11.7%)

simplify4.0ms (0.1%)

end126.0ms (1.8%)

Profiling