Details

analyze695.0ms (17%)

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
25%	74.9%	0.1%	5
37.4%	62.4%	0.1%	6
46.8%	53%	0.1%	7
52.3%	47.6%	0.1%	8
65.5%	34.3%	0.1%	9
71%	28.9%	0.1%	10
75%	24.9%	0.1%	11
81.6%	18.2%	0.1%	12
84.5%	15.4%	0.1%	13
86.9%	13%	0.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample42.0ms (1%)

Algorithm

1×

intervals

Results

23.0ms

256×

body

128

valid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify161.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

2495×	`fma-neg_binary64`
1241×	`fma-def_binary64`
1051×	`div-sub_binary64`
520×	`unswap-sqr_binary64`
430×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	20	18
2	31	18
3	48	18
4	71	18
5	103	18
6	155	18
7	209	18
8	270	18
9	300	16
10	389	16
11	599	16
12	934	16
13	1583	16
14	1525	16
15	1839	16
16	1745	16
17	1773	16
18	1933	16
19	2758	16
20	3102	16
21	4012	16
22	4885	16
23	4851	16

prune7.0ms (0.2%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
▶	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))

Compiler

Compiled 84 to 56 computations (33.3% saved)

localize16.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	0.1b	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
✓	0.2b	(/.f64 -5641895835477563/5000000000000000 y)

series204.0ms (5%)

Counts

3 → 72

Calls

3 calls:

103.0ms

(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))

98.0ms

(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))

2.0ms

(/.f64 -5641895835477563/5000000000000000 y)

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 75

Calls

3 calls:

11.0ms

(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))

5.0ms

(/.f64 -5641895835477563/5000000000000000 y)

4.0ms

(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))

simplify252.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

753×	`associate-/l*_binary64`
483×	`fma-def_binary64`
213×	`fma-neg_binary64`
189×	`distribute-rgt-in_binary64`
149×	`associate-/l/_binary64`

Counts

147 → 137

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	3584
1	599	3514
2	1868	3402
3	4874	3394
4	4971	3394

prune204.0ms (5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	136	3	139

Error

Counts

139 → 3

Alt Table

Status	Error	Program
▶	2.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
	13.3b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))))
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))

Compiler

Compiled 3376 to 2123 computations (37.1% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
✓	0.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
✓	0.6b	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
✓	6.7b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series200.0ms (4.9%)

Counts

4 → 112

Calls

4 calls:

88.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
85.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
22.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
5.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

rewrite51.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 84

Calls

4 calls:

16.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
13.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
7.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
7.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

simplify204.0ms (5%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-def_binary64`
270×	`fma-neg_binary64`
253×	`associate-/r/_binary64`
229×	`cancel-sign-sub-inv_binary64`
155×	`associate-/l/_binary64`

Counts

196 → 208

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	252	4366
1	671	4279
2	2246	4156
3	4858	4146
4	4953	4146

prune163.0ms (4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	208	3	211

Error

Counts

211 → 3

Alt Table

Status	Error	Program
✓	2.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
▶	13.3b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))))
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))

Compiler

Compiled 4805 to 2471 computations (48.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))
✓	0.0b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))))
✓	0.1b	(/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y))))
✓	0.3b	(*.f64 5641895835477563/5000000000000000 (/.f64 1 y))

series38.0ms (0.9%)

Counts

4 → 66

Calls

4 calls:

18.0ms	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))))
13.0ms	(/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y))))
5.0ms	(-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))
2.0ms	(*.f64 5641895835477563/5000000000000000 (/.f64 1 y))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`
15×	`add-exp-log_binary64`

Counts

4 → 106

Calls

4 calls:

7.0ms	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))))
6.0ms	(*.f64 5641895835477563/5000000000000000 (/.f64 1 y))
4.0ms	(/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y))))
3.0ms	(-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))

simplify122.0ms (3%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
538×	`fma-def_binary64`
450×	`associate-l_binary64`
418×	`associate-r_binary64`
204×	`associate-/r*_binary64`

Counts

172 → 205

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	216	2495
1	505	2363
2	1257	2326
3	4593	2326
4	5106	2326

prune278.0ms (6.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	205	3	208

Error

Counts

208 → 3

Alt Table

Status	Error	Program
✓	2.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
✓	13.3b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 1 y)))))
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))

Compiler

Compiled 3761 to 2731 computations (27.4% saved)

regimes144.0ms (3.5%)

Accuracy

Total 0.0b remaining (58.1%)

Threshold costs 0.0b (58.1%)

Counts

26 → 1

Compiler

Compiled 1995 to 1436 computations (28% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	12	16
2	12	16

end1.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

sample1.2s (29.9%)

Algorithm

1×

intervals

Results

733.0ms

8000×

body

128

valid

Compiler

Compiled 76 to 55 computations (27.6% saved)

Details

analyze695.0ms (17%)

sample42.0ms (1%)

simplify161.0ms (3.9%)

prune7.0ms (0.2%)

localize16.0ms (0.4%)

series204.0ms (5%)

rewrite27.0ms (0.7%)

simplify252.0ms (6.2%)

prune204.0ms (5%)

localize16.0ms (0.4%)

series200.0ms (4.9%)

rewrite51.0ms (1.3%)

simplify204.0ms (5%)

prune163.0ms (4%)

localize9.0ms (0.2%)

series38.0ms (0.9%)

rewrite27.0ms (0.6%)

simplify122.0ms (3%)

prune278.0ms (6.8%)

regimes144.0ms (3.5%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample1.2s (29.9%)

Profiling