Details

analyze365.0ms (7.2%)

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
0%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
9.4%	65.5%	25.1%	8
14%	35.9%	50.1%	9
21.1%	28.9%	50.1%	10
24.6%	25.4%	50.1%	11
28.7%	21.3%	50.1%	12
33.4%	16.5%	50.1%	13
35.8%	14.1%	50.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.2s (23.2%)

Results

1.0s	8256×	body	128	valid
4.0ms	34×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify129.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-neg_binary64`
610×	`unsub-neg_binary64`
567×	`distribute-rgt-in_binary64`
442×	`sub-neg_binary64`
412×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	25	18
2	75	16
3	253	16
4	654	16
5	1767	16
6	2167	16
7	2284	16
8	2375	16
9	2374	16
10	2391	16
11	2701	16
12	3417	16
13	4877	16
14	4713	16
15	4967	16

prune3.0ms (0.1%)

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
	0.1b	(-.f64 y (-.f64 (fma.f64 (+.f64 y 1/2) (log.f64 y) z) x))
▶	0.1b	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)

Compiler

Compiled 84 to 53 computations (36.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series168.0ms (3.3%)

Counts

3 → 60

Calls

3 calls:

82.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
76.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
10.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`log-prod_binary64`
10×	`add-log-exp_binary64`

Counts

3 → 80

Calls

3 calls:

7.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
4.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
3.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

simplify105.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

716×	`fma-def_binary64`
387×	`exp-sum_binary64`
347×	`sub-neg_binary64`
264×	`associate-+l+_binary64`
234×	`exp-diff_binary64`

Counts

140 → 161

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	174	1936
1	464	1769
2	1414	1628
3	3679	1628
4	4494	1627
5	4829	1627

prune137.0ms (2.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	155	6	161
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	157	6	163

Error

Counts

163 → 6

Alt Table

Status	Error	Program
	37.4b	(-.f64 (cbrt.f64 (pow.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) 3)) z)
	32.5b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (+.f64 y 1/2) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)))) y) z)
	0.6b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (+.f64 y 1/2) (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (log.f64 y)))) y) z)
	0.1b	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 1/2 y) (log.f64 y))) y) z)
▶	0.1b	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
	0.2b	(-.f64 (+.f64 (-.f64 (fma.f64 (.f64 (log.f64 (cbrt.f64 y)) 2) (-.f64 -1/2 y) x) (.f64 (log.f64 (cbrt.f64 y)) (+.f64 y 1/2))) y) z)

Compiler

Compiled 3219 to 1757 computations (45.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)
✓	0.2b	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

series52.0ms (1%)

Counts

2 → 36

Calls

2 calls:

43.0ms	(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)
9.0ms	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 28

Calls

2 calls:

2.0ms	(+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x)
0.0ms	(fma.f64 (log.f64 y) (-.f64 -1/2 y) y)

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

593×	`sub-neg_binary64`
376×	`unsub-neg_binary64`
363×	`+-commutative_binary64`
356×	`associate-l_binary64`
324×	`associate-r_binary64`

Counts

64 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	895
1	221	860
2	548	791
3	1679	791
4	3642	791
5	5049	791

prune49.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	54	6	60

Error

Counts

60 → 6

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 (*.f64 (log.f64 y) (-.f64 -1/2 y)) (+.f64 y x)) z)
✓	0.1b	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
	37.4b	(-.f64 (cbrt.f64 (pow.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) 3)) z)
	32.5b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (+.f64 y 1/2) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)))) y) z)
	0.6b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (+.f64 y 1/2) (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (log.f64 y)))) y) z)
	0.2b	(-.f64 (+.f64 (-.f64 (fma.f64 (.f64 (log.f64 (cbrt.f64 y)) 2) (-.f64 -1/2 y) x) (.f64 (log.f64 (cbrt.f64 y)) (+.f64 y 1/2))) y) z)

Compiler

Compiled 1155 to 646 computations (44.1% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series89.0ms (1.7%)

Counts

2 → 36

Calls

2 calls:

81.0ms	(+.f64 (*.f64 (log.f64 y) (-.f64 -1/2 y)) (+.f64 y x))
8.0ms	(*.f64 (log.f64 y) (-.f64 -1/2 y))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`prod-diff_binary64`
36×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
32×	`add-cube-cbrt_binary64`
26×	`distribute-lft-in_binary64`

Counts

2 → 97

Calls

2 calls:

8.0ms	(*.f64 (log.f64 y) (-.f64 -1/2 y))
8.0ms	(+.f64 (*.f64 (log.f64 y) (-.f64 -1/2 y)) (+.f64 y x))

simplify93.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

362×	`associate-+l+_binary64`
348×	`cancel-sign-sub-inv_binary64`
294×	`associate-+r+_binary64`
257×	`fma-neg_binary64`
233×	`associate-l_binary64`

Counts

133 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	226	2261
1	533	2044
2	2107	1877
3	4614	1877
4	4913	1877

prune127.0ms (2.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	161	6	167

Error

Counts

167 → 6

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 (*.f64 (log.f64 y) (-.f64 -1/2 y)) (+.f64 y x)) z)
✓	0.1b	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)
	37.4b	(-.f64 (cbrt.f64 (pow.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) 3)) z)
	32.5b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (+.f64 y 1/2) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)))) y) z)
	0.6b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (+.f64 y 1/2) (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (log.f64 y)))) y) z)
▶	0.2b	(-.f64 (+.f64 (-.f64 (fma.f64 (.f64 (log.f64 (cbrt.f64 y)) 2) (-.f64 -1/2 y) x) (.f64 (log.f64 (cbrt.f64 y)) (+.f64 y 1/2))) y) z)

Compiler

Compiled 4115 to 1791 computations (56.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 (-.f64 (fma.f64 (.f64 (log.f64 (cbrt.f64 y)) 2) (-.f64 -1/2 y) x) (.f64 (log.f64 (cbrt.f64 y)) (+.f64 y 1/2))) y)
✓	0.1b	(*.f64 (log.f64 (cbrt.f64 y)) (+.f64 y 1/2))
✓	0.2b	(-.f64 (fma.f64 (.f64 (log.f64 (cbrt.f64 y)) 2) (-.f64 -1/2 y) x) (.f64 (log.f64 (cbrt.f64 y)) (+.f64 y 1/2)))
✓	0.6b	(cbrt.f64 y)

series1.7s (33%)

Counts

4 → 72

Calls

4 calls:

839.0ms	(+.f64 (-.f64 (fma.f64 (.f64 (log.f64 (cbrt.f64 y)) 2) (-.f64 -1/2 y) x) (.f64 (log.f64 (cbrt.f64 y)) (+.f64 y 1/2))) y)
666.0ms	(-.f64 (fma.f64 (.f64 (log.f64 (cbrt.f64 y)) 2) (-.f64 -1/2 y) x) (.f64 (log.f64 (cbrt.f64 y)) (+.f64 y 1/2)))
135.0ms	(*.f64 (log.f64 (cbrt.f64 y)) (+.f64 y 1/2))
32.0ms	(cbrt.f64 y)

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`
7×	`pow1_binary64`

Counts

4 → 88

Calls

4 calls:

5.0ms	(*.f64 (log.f64 (cbrt.f64 y)) (+.f64 y 1/2))
5.0ms	(+.f64 (-.f64 (fma.f64 (.f64 (log.f64 (cbrt.f64 y)) 2) (-.f64 -1/2 y) x) (.f64 (log.f64 (cbrt.f64 y)) (+.f64 y 1/2))) y)
2.0ms	(-.f64 (fma.f64 (.f64 (log.f64 (cbrt.f64 y)) 2) (-.f64 -1/2 y) x) (.f64 (log.f64 (cbrt.f64 y)) (+.f64 y 1/2)))
1.0ms	(cbrt.f64 y)

simplify156.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

809×	`distribute-rgt-in_binary64`
527×	`fma-neg_binary64`
412×	`cancel-sign-sub-inv_binary64`
195×	`exp-prod_binary64`
184×	`distribute-rgt-neg-in_binary64`

Counts

160 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	185	3429
1	483	2820
2	1748	2581
3	4399	2581
4	4954	2581
5	4991	2581
6	4870	2581

prune172.0ms (3.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	2	3
Picked	1	0	1
Done	1	1	2
Total	185	4	189

Error

Counts

189 → 4

Alt Table

Status	Error	Program
	32.5b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (+.f64 y 1/2) (sqrt.f64 (log.f64 y))) (sqrt.f64 (log.f64 y)))) y) z)
	0.6b	(-.f64 (+.f64 (-.f64 x (.f64 (.f64 (+.f64 y 1/2) (*.f64 (cbrt.f64 (log.f64 y)) (cbrt.f64 (log.f64 y)))) (cbrt.f64 (log.f64 y)))) y) z)
	0.2b	(-.f64 (+.f64 (fma.f64 (*.f64 (log.f64 (cbrt.f64 y)) 2) (-.f64 -1/2 y) x) (fma.f64 (log.f64 (cbrt.f64 y)) (-.f64 -1/2 y) y)) z)
✓	0.1b	(-.f64 (+.f64 (fma.f64 (log.f64 y) (-.f64 -1/2 y) y) x) z)

Compiler

Compiled 5465 to 3000 computations (45.1% saved)

regimes345.0ms (6.8%)

Accuracy

Total 0.1b remaining (75.6%)

Threshold costs 0.1b (75.6%)

Counts

71 → 1

Compiler

Compiled 6714 to 4552 computations (32.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	15	16
2	23	16
3	27	16
4	29	16
5	29	16

end66.0ms (1.3%)

Compiler: Compiled 110 to 67 computations (39.1% saved)

Details

analyze365.0ms (7.2%)

sample1.2s (23.2%)

simplify129.0ms (2.5%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series168.0ms (3.3%)

rewrite18.0ms (0.3%)

simplify105.0ms (2.1%)

prune137.0ms (2.7%)

localize8.0ms (0.2%)

series52.0ms (1%)

rewrite4.0ms (0.1%)

simplify65.0ms (1.3%)

prune49.0ms (1%)

localize8.0ms (0.2%)

series89.0ms (1.7%)

rewrite24.0ms (0.5%)

simplify93.0ms (1.8%)

prune127.0ms (2.5%)

localize13.0ms (0.3%)

series1.7s (33%)

rewrite16.0ms (0.3%)

simplify156.0ms (3.1%)

prune172.0ms (3.4%)

regimes345.0ms (6.8%)

simplify2.0ms (0%)

end66.0ms (1.3%)

Profiling