Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.2s (42.5%)

Results

465.0ms	2112×	body	512	valid
415.0ms	4640×	body	128	valid
178.0ms	1086×	body	256	valid
127.0ms	418×	body	1024	valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
13×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16

prune2.0ms (0.1%)

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

15.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.8b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 47 to 39 computations (17% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x 1))
✓	0.0b	(/.f64 1 (-.f64 x 1))
✓	2.5b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

series8.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))
2.0ms	(/.f64 1 (-.f64 x 1))
2.0ms	(/.f64 1 (+.f64 x 1))

rewrite116.0ms (4%)

Algorithm

2×	batch-egg-rewrite

Rules

867×	`prod-diff_binary64`
441×	`fma-def_binary64`
272×	`fma-neg_binary64`
197×	`egg-rr`
162×	`expm1-udef_binary64`

Counts

3 → 197

Calls

3 calls:

111.0ms	(/.f64 1 (+.f64 x 1))
111.0ms	(/.f64 1 (-.f64 x 1))
111.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 (-.f64 x 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	192	30
2	2537	30
3	4910	30
4	4938	30
0	0	0
1	0	0

simplify65.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

748×	`unswap-sqr_binary64`
435×	`associate-l_binary64`
355×	`fma-neg_binary64`
344×	`associate-/r*_binary64`
301×	`associate-r_binary64`

Counts

233 → 238

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	575
1	197	543
2	573	540
3	1610	537
4	4128	537
5	5539	537

prune225.0ms (7.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	235	3	238
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	236	3	239

Error

0.2b

Counts

239 → 3

Alt Table

Status	Error	Program
	26.8b	(-.f64 (pow.f64 (pow.f64 (+.f64 1 x) -1/2) 2) (/.f64 1 (-.f64 x 1)))
	31.8b	(-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 2 (pow.f64 x 4)))
▶	15.2b	(/.f64 (/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (+.f64 1 x)) (-.f64 x 1))

Compiler

Compiled 6069 to 4943 computations (18.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (+.f64 1 x))
✓	0.0b	(/.f64 (/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (+.f64 1 x)) (-.f64 x 1))
✓	1.9b	(-.f64 (-.f64 x 1) (+.f64 1 x))

series7.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(/.f64 (/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (+.f64 1 x)) (-.f64 x 1))
3.0ms	(/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (+.f64 1 x))
1.0ms	(-.f64 (-.f64 x 1) (+.f64 1 x))

rewrite104.0ms (3.6%)

Algorithm

2×	batch-egg-rewrite

Rules

915×	`prod-diff_binary64`
244×	`egg-rr`
177×	`log1p-udef_binary64`
102×	`add-sqr-sqrt_binary64`
100×	`log1p-expm1-u_binary64`

Counts

3 → 244

Calls

3 calls:

98.0ms	(/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (+.f64 1 x))
98.0ms	(/.f64 (/.f64 (-.f64 (-.f64 x 1) (+.f64 1 x)) (+.f64 1 x)) (-.f64 x 1))
98.0ms	(-.f64 (-.f64 x 1) (+.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	48
1	201	34
2	3141	34
3	5187	34
0	0	0
1	0	0

simplify87.0ms (3%)

Algorithm

1×	egg-herbie

Rules

453×	`times-frac_binary64`
453×	`fma-neg_binary64`
428×	`div-sub_binary64`
355×	`unswap-sqr_binary64`
339×	`associate-/r*_binary64`

Counts

280 → 273

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	421
1	178	401
2	514	392
3	1549	387
4	4295	387
5	4931	387
6	5471	387

prune198.0ms (6.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	272	1	273
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	273	3	276

Error

0.0b

Counts

276 → 3

Alt Table

Status	Error	Program
	26.8b	(-.f64 (pow.f64 (pow.f64 (+.f64 1 x) -1/2) 2) (/.f64 1 (-.f64 x 1)))
	31.8b	(-.f64 (/.f64 -2 (*.f64 x x)) (/.f64 2 (pow.f64 x 4)))
▶	0.1b	(/.f64 (/.f64 -2 (+.f64 1 x)) (-.f64 x 1))

Compiler

Compiled 7643 to 5432 computations (28.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 -2 (+.f64 1 x))
✓	0.1b	(/.f64 (/.f64 -2 (+.f64 1 x)) (-.f64 x 1))

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(/.f64 (/.f64 -2 (+.f64 1 x)) (-.f64 x 1))
3.0ms	(/.f64 -2 (+.f64 1 x))

rewrite93.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

421×	`log-prod_binary64`
385×	`prod-diff_binary64`
207×	`fma-def_binary64`
195×	`log-div_binary64`
158×	`expm1-udef_binary64`

Counts

2 → 70

Calls

2 calls:

92.0ms	(/.f64 -2 (+.f64 1 x))
92.0ms	(/.f64 (/.f64 -2 (+.f64 1 x)) (-.f64 x 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	187	15
2	2480	15
3	4961	15
4	5363	15
0	0	0
1	0	0

simplify75.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

453×	`times-frac_binary64`
453×	`fma-neg_binary64`
428×	`div-sub_binary64`
355×	`unswap-sqr_binary64`
339×	`associate-/r*_binary64`

Counts

94 → 99

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	409
1	178	389
2	514	380
3	1549	375
4	4295	375
5	4931	375
6	5471	375

prune79.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	92	7	99
Fresh	2	0	2
Picked	0	1	1
Done	0	0	0
Total	94	8	102

Error

Counts

102 → 8

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 0 (/.f64 -2 (fma.f64 x x -1)))
	12.8b	(cbrt.f64 (pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3))
	1.5b	(pow.f64 (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))) 3)
	23.3b	(*.f64 (/.f64 (/.f64 -2 (+.f64 1 x)) (+.f64 (pow.f64 x 3) -1)) (fma.f64 x x (+.f64 1 x)))
	49.8b	(*.f64 (/.f64 (sqrt.f64 (/.f64 -2 (+.f64 1 x))) 1) (/.f64 (sqrt.f64 (/.f64 -2 (+.f64 1 x))) (-.f64 x 1)))
	1.3b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 -2 (+.f64 1 x))) 2) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))))
	0.4b	(*.f64 (/.f64 -2 (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)) (/.f64 (/.f64 1 (+.f64 1 x)) (cbrt.f64 (-.f64 x 1))))
✓	0.1b	(/.f64 (/.f64 -2 (+.f64 1 x)) (-.f64 x 1))

Compiler

Compiled 1623 to 1301 computations (19.8% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 -2 (fma.f64 x x -1))

series5.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

5.0ms

(/.f64 -2 (fma.f64 x x -1))

rewrite75.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

502×	`log1p-expm1-u_binary64`
502×	`expm1-log1p-u_binary64`
260×	`unpow-prod-down_binary64`
229×	`log-prod_binary64`
145×	`pow2_binary64`

Counts

1 → 38

Calls

1 calls:

74.0ms

(/.f64 -2 (fma.f64 x x -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	122	8
2	1320	8
3	4941	8
4	5055	8
0	0	0
1	0	0

simplify65.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

675×	`fma-def_binary64`
414×	`unswap-sqr_binary64`
344×	`distribute-neg-frac_binary64`
327×	`div-sub_binary64`
243×	`associate-l_binary64`

Counts

50 → 53

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	227
1	116	209
2	328	206
3	957	203
4	2990	200
5	4474	200
6	4946	200

prune55.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	53	8	61

Error

Counts

61 → 8

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 0 (/.f64 -2 (fma.f64 x x -1)))
	12.8b	(cbrt.f64 (pow.f64 (/.f64 -2 (fma.f64 x x -1)) 3))
	1.5b	(pow.f64 (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))) 3)
	23.3b	(*.f64 (/.f64 (/.f64 -2 (+.f64 1 x)) (+.f64 (pow.f64 x 3) -1)) (fma.f64 x x (+.f64 1 x)))
	49.8b	(*.f64 (/.f64 (sqrt.f64 (/.f64 -2 (+.f64 1 x))) 1) (/.f64 (sqrt.f64 (/.f64 -2 (+.f64 1 x))) (-.f64 x 1)))
	1.3b	(*.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 -2 (+.f64 1 x))) 2) (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)) (cbrt.f64 (/.f64 -2 (fma.f64 x x -1))))
	0.4b	(*.f64 (/.f64 -2 (pow.f64 (cbrt.f64 (-.f64 x 1)) 2)) (/.f64 (/.f64 1 (+.f64 1 x)) (cbrt.f64 (-.f64 x 1))))
✓	0.1b	(/.f64 (/.f64 -2 (+.f64 1 x)) (-.f64 x 1))

Compiler

Compiled 912 to 743 computations (18.5% saved)

regimes234.0ms (8.2%)

Accuracy

Total 0.1b remaining (87.4%)

Threshold costs 0.1b (87.4%)

Counts

133 → 1

Compiler

Compiled 4370 to 3602 computations (17.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	14	13
2	15	13
3	13	13

end108.0ms (3.8%)

Compiler: Compiled 142 to 115 computations (19% saved)

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16

Details

analyze4.0ms (0.2%)

sample1.2s (42.5%)

simplify13.0ms (0.4%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series8.0ms (0.3%)

rewrite116.0ms (4%)

simplify65.0ms (2.3%)

prune225.0ms (7.8%)

localize6.0ms (0.2%)

series7.0ms (0.3%)

rewrite104.0ms (3.6%)

simplify87.0ms (3%)

prune198.0ms (6.9%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite93.0ms (3.2%)

simplify75.0ms (2.6%)

prune79.0ms (2.8%)

localize4.0ms (0.2%)

series5.0ms (0.2%)

rewrite75.0ms (2.6%)

simplify65.0ms (2.3%)

prune55.0ms (1.9%)

regimes234.0ms (8.2%)

simplify2.0ms (0.1%)

end108.0ms (3.8%)

Profiling

Iter	Nodes	Cost
0	8	16
1	16	16
2	21	16
3	29	16
4	37	16
5	55	16
6	80	16
7	97	16
8	114	16
9	124	16
10	128	16
11	130	16
12	116	16