Details

analyze411.0ms (2.7%)

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%	87.4%	12.6%	5
0%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
12.5%	56.2%	31.4%	8
14%	48.4%	37.6%	9
21.1%	41.3%	37.6%	10
26.9%	32.4%	40.7%	11
28.7%	27.5%	43.8%	12
33.4%	22.7%	43.8%	13
37.2%	17.4%	45.4%	14

Compiler

Compiled 12 to 8 computations (33.3% saved)

sample1.3s (8.5%)

Results

972.0ms	8256×	body	128	valid
76.0ms	761×	body	128	invalid

Compiler

Compiled 35 to 23 computations (34.3% saved)

simplify203.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

2528×	`fma-neg_binary64`
1701×	`fma-def_binary64`
364×	`distribute-rgt-in_binary64`
336×	`unsub-neg_binary64`
328×	`associate--r-_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	15	12
2	23	12
3	39	12
4	85	12
5	184	12
6	322	12
7	518	12
8	681	12
9	1097	12
10	1783	12
11	1812	12
12	1882	12
13	1916	12
14	1930	12
15	3312	12
16	4220	12
17	3919	12
18	4053	12
19	4118	12
20	4154	12
21	4164	12
22	4224	12
23	4182	12
24	4182	12
25	5994	12

prune2.0ms (0%)

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

13.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	13.9b	(-.f64 (*.f64 x (log.f64 (/.f64 x y))) z)

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 x (log.f64 (/.f64 x y))) z)
✓	0.3b	(*.f64 x (log.f64 (/.f64 x y)))
✓	13.5b	(log.f64 (/.f64 x y))

series877.0ms (5.8%)

Counts

3 → 84

Calls

3 calls:

340.0ms	(*.f64 x (log.f64 (/.f64 x y)))
313.0ms	(log.f64 (/.f64 x y))
225.0ms	(-.f64 (*.f64 x (log.f64 (/.f64 x y))) z)

rewrite64.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

916×	`expm1-log1p-u_binary64`
642×	`prod-diff_binary64`
143×	`egg-rr`
90×	`add-sqr-sqrt_binary64`
85×	`log1p-expm1-u_binary64`

Counts

3 → 143

Calls

3 calls:

61.0ms	(-.f64 (*.f64 x (log.f64 (/.f64 x y))) z)
61.0ms	(*.f64 x (log.f64 (/.f64 x y)))
61.0ms	(log.f64 (/.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	173	27
2	2303	27
3	5175	27
0	0	0
1	0	0

simplify346.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

2467×	`fma-neg_binary64`
510×	`distribute-rgt-in_binary64`
508×	`sub-neg_binary64`
506×	`unsub-neg_binary64`
472×	`associate--r-_binary64`

Counts

227 → 162

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	756
1	120	756
2	249	756
3	563	756
4	1375	756
5	1807	756
6	1950	756
7	1863	756
8	1927	756
9	1881	756
10	1889	756
11	1975	756
12	1941	756
13	1939	756
14	1939	756
15	4495	756
16	4326	756
17	4450	756
18	4590	756
19	4635	756
20	4639	756
21	4721	756
22	4681	756
23	4693	756
24	4733	756
25	4807	756
26	5096	756

prune105.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	154	8	162
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	154	9	163

Error

0.0b

Counts

163 → 9

Alt Table

Status	Error	Program
	29.0b	(-.f64 (.f64 (log.f64 x) x) (+.f64 (.f64 (log.f64 y) x) z))
✓	13.9b	(-.f64 (*.f64 x (log.f64 (/.f64 x y))) z)
	14.3b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 x (log.f64 (/.f64 x y)))) 2) (cbrt.f64 (.f64 x (log.f64 (/.f64 x y)))) (neg.f64 z))
▶	13.9b	(-.f64 (*.f64 x (+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) (log.f64 (cbrt.f64 (/.f64 x y))))) z)
	35.4b	(-.f64 (+.f64 (.f64 (log.f64 (/.f64 -1 y)) x) (.f64 (log.f64 (neg.f64 x)) x)) z)
	29.0b	(-.f64 (*.f64 x (-.f64 (log.f64 x) (log.f64 y))) z)
	35.4b	(-.f64 (*.f64 x (-.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 y)))) z)
	37.1b	(-.f64 (*.f64 x (-.f64 (exp.f64 (log1p.f64 (log.f64 (/.f64 x y)))) 1)) z)
	29.3b	(-.f64 (.f64 x (+.f64 (fma.f64 1 (log.f64 x) (neg.f64 (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))))))) z)

Compiler

Compiled 3143 to 898 computations (71.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 x (+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) (log.f64 (cbrt.f64 (/.f64 x y)))))
✓	0.5b	(pow.f64 (cbrt.f64 (/.f64 x y)) 2)
✓	1.7b	(log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2))
✓	13.9b	(cbrt.f64 (/.f64 x y))

series5.2s (34.1%)

Counts

4 → 96

Calls

4 calls:

2.9s	(*.f64 x (+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) (log.f64 (cbrt.f64 (/.f64 x y)))))
1.6s	(log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2))
347.0ms	(pow.f64 (cbrt.f64 (/.f64 x y)) 2)
324.0ms	(cbrt.f64 (/.f64 x y))

rewrite64.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

959×	`prod-diff_binary64`
194×	`log1p-udef_binary64`
114×	`add-sqr-sqrt_binary64`
109×	`add-log-exp_binary64`
109×	`log1p-expm1-u_binary64`

Counts

4 → 108

Calls

4 calls:

62.0ms	(*.f64 x (+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) (log.f64 (cbrt.f64 (/.f64 x y)))))
62.0ms	(pow.f64 (cbrt.f64 (/.f64 x y)) 2)
62.0ms	(log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2))
62.0ms	(cbrt.f64 (/.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	233	35
2	2853	35
3	4967	35
0	0	0
1	0	0

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-def_binary64`
592×	`associate-l_binary64`
340×	`unswap-sqr_binary64`
340×	`fma-neg_binary64`
293×	`distribute-rgt-in_binary64`

Counts

204 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	2408
1	158	2200
2	326	1784
3	1233	1224
4	4994	1224
5	5131	1224

prune148.0ms (1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	178	10	188

Error

0.0b

Counts

188 → 10

Alt Table

Status	Error	Program
	29.0b	(-.f64 (.f64 (log.f64 x) x) (+.f64 (.f64 (log.f64 y) x) z))
✓	13.9b	(-.f64 (*.f64 x (log.f64 (/.f64 x y))) z)
	14.3b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 x (log.f64 (/.f64 x y)))) 2) (cbrt.f64 (.f64 x (log.f64 (/.f64 x y)))) (neg.f64 z))
✓	13.9b	(-.f64 (*.f64 x (+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) (log.f64 (cbrt.f64 (/.f64 x y))))) z)
	35.4b	(-.f64 (+.f64 (.f64 (log.f64 (/.f64 -1 y)) x) (.f64 (log.f64 (neg.f64 x)) x)) z)
	29.0b	(-.f64 (*.f64 x (-.f64 (log.f64 x) (log.f64 y))) z)
	35.4b	(-.f64 (*.f64 x (-.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 y)))) z)
	37.1b	(-.f64 (*.f64 x (-.f64 (exp.f64 (log1p.f64 (log.f64 (/.f64 x y)))) 1)) z)
▶	14.0b	(-.f64 (/.f64 (.f64 (+.f64 (pow.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) 3) (pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 3)) x) (+.f64 (pow.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) 2) (-.f64 (pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 2) (.f64 2 (pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 2))))) z)
	29.3b	(-.f64 (.f64 x (+.f64 (fma.f64 1 (log.f64 x) (neg.f64 (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))))))) z)

Compiler

Compiled 4320 to 2045 computations (52.7% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(pow.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) 3)
✓	0.7b	(pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 3)
	1.7b	(log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2))
	13.9b	(cbrt.f64 (/.f64 x y))

series2.9s (19.5%)

Counts

2 → 48

Calls

2 calls:

1.7s	(pow.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) 3)
1.3s	(pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 3)

rewrite85.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

505×	`log-prod_binary64`
266×	`pow2_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`
183×	`pow1/3_binary64`

Counts

2 → 49

Calls

2 calls:

84.0ms	(pow.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) 3)
84.0ms	(pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	243	25
2	2521	23
3	4980	23
4	5078	23
0	0	0
1	0	0

simplify64.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

598×	`log-prod_binary64`
500×	`fma-def_binary64`
352×	`unswap-sqr_binary64`
247×	`associate-+l+_binary64`
213×	`distribute-rgt-neg-out_binary64`

Counts

97 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	65	1040
1	175	944
2	370	840
3	1479	720
4	4611	720
5	5526	720

prune450.0ms (3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	337	0	337
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	337	10	347

Error

0.0b

Counts

347 → 10

Alt Table

Status	Error	Program
	29.0b	(-.f64 (.f64 (log.f64 x) x) (+.f64 (.f64 (log.f64 y) x) z))
✓	13.9b	(-.f64 (*.f64 x (log.f64 (/.f64 x y))) z)
▶	14.3b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 x (log.f64 (/.f64 x y)))) 2) (cbrt.f64 (.f64 x (log.f64 (/.f64 x y)))) (neg.f64 z))
✓	13.9b	(-.f64 (*.f64 x (+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) (log.f64 (cbrt.f64 (/.f64 x y))))) z)
	35.4b	(-.f64 (+.f64 (.f64 (log.f64 (/.f64 -1 y)) x) (.f64 (log.f64 (neg.f64 x)) x)) z)
	29.0b	(-.f64 (*.f64 x (-.f64 (log.f64 x) (log.f64 y))) z)
	35.4b	(-.f64 (*.f64 x (-.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 y)))) z)
	37.1b	(-.f64 (*.f64 x (-.f64 (exp.f64 (log1p.f64 (log.f64 (/.f64 x y)))) 1)) z)
✓	14.0b	(-.f64 (/.f64 (.f64 (+.f64 (pow.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) 3) (pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 3)) x) (+.f64 (pow.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) 2) (-.f64 (pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 2) (.f64 2 (pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 2))))) z)
	29.3b	(-.f64 (.f64 x (+.f64 (fma.f64 1 (log.f64 x) (neg.f64 (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))))))) z)

Compiler

Compiled 18574 to 9657 computations (48% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 x (log.f64 (/.f64 x y)))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 (/.f64 x y)))) 2)
✓	0.6b	(cbrt.f64 (*.f64 x (log.f64 (/.f64 x y))))
	13.5b	(log.f64 (/.f64 x y))

series1.6s (10.9%)

Counts

2 → 48

Calls

2 calls:

833.0ms	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 (/.f64 x y)))) 2)
808.0ms	(cbrt.f64 (*.f64 x (log.f64 (/.f64 x y))))

rewrite48.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

777×	`log1p-expm1-u_binary64`
777×	`expm1-log1p-u_binary64`
151×	`log1p-udef_binary64`
87×	`add-sqr-sqrt_binary64`
82×	`add-log-exp_binary64`

Counts

2 → 48

Calls

2 calls:

47.0ms	(pow.f64 (cbrt.f64 (*.f64 x (log.f64 (/.f64 x y)))) 2)
47.0ms	(cbrt.f64 (*.f64 x (log.f64 (/.f64 x y))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	182	25
2	2043	25
3	5037	25
0	0	0
1	0	0

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

728×	`associate-l_binary64`
657×	`associate-r_binary64`
421×	`distribute-rgt-in_binary64`
398×	`distribute-lft-in_binary64`
277×	`unswap-sqr_binary64`

Counts

96 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	59	1152
1	130	1152
2	267	1072
3	961	872
4	4801	864
5	4999	864
6	4930	864

prune156.0ms (1%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	219	0	219
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	219	10	229

Error

0.0b

Counts

229 → 10

Alt Table

Status	Error	Program
	29.0b	(-.f64 (.f64 (log.f64 x) x) (+.f64 (.f64 (log.f64 y) x) z))
✓	13.9b	(-.f64 (*.f64 x (log.f64 (/.f64 x y))) z)
✓	14.3b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 x (log.f64 (/.f64 x y)))) 2) (cbrt.f64 (.f64 x (log.f64 (/.f64 x y)))) (neg.f64 z))
✓	13.9b	(-.f64 (*.f64 x (+.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) (log.f64 (cbrt.f64 (/.f64 x y))))) z)
	35.4b	(-.f64 (+.f64 (.f64 (log.f64 (/.f64 -1 y)) x) (.f64 (log.f64 (neg.f64 x)) x)) z)
	29.0b	(-.f64 (*.f64 x (-.f64 (log.f64 x) (log.f64 y))) z)
	35.4b	(-.f64 (*.f64 x (-.f64 (log.f64 (neg.f64 x)) (log.f64 (neg.f64 y)))) z)
	37.1b	(-.f64 (*.f64 x (-.f64 (exp.f64 (log1p.f64 (log.f64 (/.f64 x y)))) 1)) z)
✓	14.0b	(-.f64 (/.f64 (.f64 (+.f64 (pow.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) 3) (pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 3)) x) (+.f64 (pow.f64 (log.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2)) 2) (-.f64 (pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 2) (.f64 2 (pow.f64 (log.f64 (cbrt.f64 (/.f64 x y))) 2))))) z)
	29.3b	(-.f64 (.f64 x (+.f64 (fma.f64 1 (log.f64 x) (neg.f64 (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))))) (fma.f64 (neg.f64 (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))) (.f64 (cbrt.f64 (log.f64 y)) (.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y))))))) z)

Compiler

Compiled 5766 to 1751 computations (69.6% saved)

regimes626.0ms (4.1%)

Accuracy

Total 0.3b remaining (88.7%)

Threshold costs 0.3b (88.7%)

Counts

53 → 2

Compiler

Compiled 6077 to 3576 computations (41.2% saved)

bsearch45.0ms (0.3%)

Steps

Iters	Range		Point
10	-1.936072670683473e-304	1.2060448922357308e-300	-4.3772205150223e-310

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
10×	`*-commutative_binary64`
10×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	41
1	37	41
2	53	41
3	70	41
4	77	41
5	80	41
6	81	41
7	81	41

end177.0ms (1.2%)

Compiler: Compiled 282 to 164 computations (41.8% saved)

Details

analyze411.0ms (2.7%)

sample1.3s (8.5%)

simplify203.0ms (1.3%)

prune2.0ms (0%)

localize6.0ms (0%)

series877.0ms (5.8%)

rewrite64.0ms (0.4%)

simplify346.0ms (2.3%)

prune105.0ms (0.7%)

localize12.0ms (0.1%)

series5.2s (34.1%)

rewrite64.0ms (0.4%)

simplify83.0ms (0.5%)

prune148.0ms (1%)

localize24.0ms (0.2%)

series2.9s (19.5%)

rewrite85.0ms (0.6%)

simplify64.0ms (0.4%)

prune450.0ms (3%)

localize10.0ms (0.1%)

series1.6s (10.9%)

rewrite48.0ms (0.3%)

simplify83.0ms (0.5%)

prune156.0ms (1%)

regimes626.0ms (4.1%)

bsearch45.0ms (0.3%)

simplify5.0ms (0%)

end177.0ms (1.2%)

Profiling