Details

analyze51.0ms (2.8%)

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
25%	74.9%	0.1%	4
43.7%	56.2%	0.1%	5
65.6%	34.3%	0.1%	6
76.5%	23.4%	0.1%	7
82%	18%	0.1%	8
87.8%	12.1%	0.1%	9
90.7%	9.2%	0.1%	10
93.8%	6.1%	0.1%	11
95.3%	4.6%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 8 to 5 computations (37.5% saved)

sample660.0ms (36.1%)

Results

634.0ms

8256×

body

128

valid

Compiler

Compiled 23 to 14 computations (39.1% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	6	7
2	6	7

prune5.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 26 to 14 computations (46.2% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

9.0ms

(/.f64 x (+.f64 y x))

rewrite42.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

664×	`log1p-expm1-u_binary64`
664×	`expm1-log1p-u_binary64`
473×	`prod-diff_binary64`
61×	`add-sqr-sqrt_binary64`
57×	`add-log-exp_binary64`

Counts

1 → 35

Calls

1 calls:

42.0ms

(/.f64 x (+.f64 y x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	115	7
2	1646	7
3	4975	7
0	0	0
1	0	0

simplify68.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

385×	`associate-/l*_binary64`
334×	`associate-/r*_binary64`
321×	`associate-*l/_binary64`
252×	`fma-def_binary64`
241×	`associate-*r/_binary64`

Counts

59 → 48

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	30	438
1	76	438
2	217	387
3	866	345
4	4256	345
5	4966	321
6	4952	321

prune31.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	45	4	49

Error

Counts

49 → 4

Alt Table

Status	Error	Program
	0.2b	(*.f64 x (/.f64 1 (+.f64 x y)))
✓	0.0b	(/.f64 x (+.f64 y x))
	11.2b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) 3))
▶	0.2b	(pow.f64 (/.f64 (+.f64 x y) x) -1)

Compiler

Compiled 597 to 263 computations (55.9% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) x)
✓	0.2b	(pow.f64 (/.f64 (+.f64 x y) x) -1)

series14.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(pow.f64 (/.f64 (+.f64 x y) x) -1)
5.0ms	(/.f64 (+.f64 x y) x)

rewrite56.0ms (3.1%)

Algorithm

2×	batch-egg-rewrite

Rules

823×	`log1p-expm1-u_binary64`
823×	`expm1-log1p-u_binary64`
473×	`prod-diff_binary64`
80×	`add-sqr-sqrt_binary64`
78×	`egg-rr`

Counts

2 → 78

Calls

2 calls:

55.0ms	(/.f64 (+.f64 x y) x)
55.0ms	(pow.f64 (/.f64 (+.f64 x y) x) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	157	14
2	2050	14
3	5890	14
0	0	0
1	0	0

simplify69.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

385×	`associate-/l*_binary64`
334×	`associate-/r*_binary64`
321×	`associate-*l/_binary64`
253×	`fma-def_binary64`
241×	`associate-*r/_binary64`

Counts

126 → 94

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	31	579
1	78	579
2	219	528
3	868	486
4	4259	486
5	4969	462
6	4955	462

prune45.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	94	4	98

Error

Counts

98 → 4

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 x (/.f64 1 (+.f64 x y)))
✓	0.0b	(/.f64 x (+.f64 y x))
	11.2b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) 3))
✓	0.2b	(pow.f64 (/.f64 (+.f64 x y) x) -1)

Compiler

Compiled 1139 to 473 computations (58.5% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x y))
✓	0.2b	(*.f64 x (/.f64 1 (+.f64 x y)))

series17.0ms (1%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(*.f64 x (/.f64 1 (+.f64 x y)))
8.0ms	(/.f64 1 (+.f64 x y))

rewrite47.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

738×	`log1p-expm1-u_binary64`
738×	`expm1-log1p-u_binary64`
484×	`prod-diff_binary64`
75×	`add-sqr-sqrt_binary64`
69×	`add-cbrt-cube_binary64`

Counts

2 → 51

Calls

2 calls:

46.0ms	(/.f64 1 (+.f64 x y))
46.0ms	(*.f64 x (/.f64 1 (+.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	151	14
2	1874	14
3	5439	14
0	0	0
1	0	0

simplify59.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-neg_binary64`
588×	`associate-/l*_binary64`
539×	`associate-/r*_binary64`
451×	`cancel-sign-sub-inv_binary64`
426×	`fma-def_binary64`

Counts

99 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	48	912
1	118	912
2	351	825
3	1338	750
4	4726	750
5	5115	750

prune37.0ms (2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	78	4	82

Error

Counts

82 → 4

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 x (/.f64 1 (+.f64 x y)))
✓	0.0b	(/.f64 x (+.f64 y x))
▶	11.2b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) 3))
✓	0.2b	(pow.f64 (/.f64 (+.f64 x y) x) -1)

Compiler

Compiled 943 to 481 computations (49% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (+.f64 x y))
✓	0.1b	(pow.f64 (/.f64 x (+.f64 x y)) 3)
✓	11.2b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) 3))

series103.0ms (5.6%)

Counts

3 → 72

Calls

3 calls:

77.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) 3))
17.0ms	(pow.f64 (/.f64 x (+.f64 x y)) 3)
9.0ms	(/.f64 x (+.f64 x y))

rewrite146.0ms (8%)

Algorithm

2×	batch-egg-rewrite

Rules

852×	`log1p-expm1-u_binary64`
852×	`expm1-log1p-u_binary64`
473×	`prod-diff_binary64`
124×	`egg-rr`
79×	`add-sqr-sqrt_binary64`

Counts

3 → 124

Calls

3 calls:

144.0ms	(/.f64 x (+.f64 x y))
144.0ms	(pow.f64 (/.f64 x (+.f64 x y)) 3)
144.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	163	24
2	2122	24
3	6029	24
0	0	0
1	0	0

simplify78.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

918×	`fma-neg_binary64`
375×	`distribute-rgt-neg-in_binary64`
371×	`times-frac_binary64`
314×	`distribute-neg-frac_binary64`
218×	`unswap-sqr_binary64`

Counts

196 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	1498
1	199	1498
2	602	1317
3	2917	1263
4	4998	1263
5	5194	1263

prune171.0ms (9.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	121	4	125

Error

Counts

125 → 4

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 x (/.f64 1 (+.f64 x y)))
✓	0.0b	(/.f64 x (+.f64 y x))
✓	11.2b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 x y)) 3))
✓	0.2b	(pow.f64 (/.f64 (+.f64 x y) x) -1)

Compiler

Compiled 1626 to 755 computations (53.6% saved)

regimes47.0ms (2.6%)

Accuracy

Total 0.0b remaining (67%)

Threshold costs 0.0b (67%)

Counts

14 → 1

Compiler

Compiled 437 to 286 computations (34.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	6	7
2	6	7

end46.0ms (2.5%)

Compiler: Compiled 49 to 31 computations (36.7% saved)

Details

analyze51.0ms (2.8%)

sample660.0ms (36.1%)

simplify6.0ms (0.3%)

prune5.0ms (0.2%)

localize3.0ms (0.2%)

series9.0ms (0.5%)

rewrite42.0ms (2.3%)

simplify68.0ms (3.7%)

prune31.0ms (1.7%)

localize4.0ms (0.2%)

series14.0ms (0.8%)

rewrite56.0ms (3.1%)

simplify69.0ms (3.8%)

prune45.0ms (2.5%)

localize4.0ms (0.2%)

series17.0ms (1%)

rewrite47.0ms (2.6%)

simplify59.0ms (3.2%)

prune37.0ms (2%)

localize5.0ms (0.3%)

series103.0ms (5.6%)

rewrite146.0ms (8%)

simplify78.0ms (4.3%)

prune171.0ms (9.4%)

regimes47.0ms (2.6%)

simplify2.0ms (0.1%)

end46.0ms (2.5%)

Profiling