Details

analyze299.0ms (12.5%)

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)

sample139.0ms (5.8%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify138.0ms (5.8%)

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

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.4b	(+.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)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series114.0ms (4.8%)

Counts

4 → 108

Calls

4 calls:

50.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
48.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
13.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
3.0ms	(/.f64 -5641895835477563/5000000000000000 y)

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 85

Calls

4 calls:

4.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
3.0ms	(/.f64 -5641895835477563/5000000000000000 y)
2.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
0.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)

simplify108.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

759×	`associate-/l*_binary64`
549×	`fma-def_binary64`
209×	`distribute-rgt-in_binary64`
152×	`associate-/l/_binary64`
149×	`distribute-lft-in_binary64`

Counts

193 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	263	4154
1	654	3971
2	1995	3895
3	5228	3895

prune121.0ms (5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	160	3	163

Error

Counts

163 → 3

Alt Table

Status	Error	Program
▶	1.4b	(+.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)))
	25.5b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

Compiler

Compiled 3769 to 2353 computations (37.6% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
✓	0.0b	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
✓	0.2b	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
✓	8.0b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series99.0ms (4.1%)

Counts

4 → 112

Calls

4 calls:

44.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
42.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
10.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
2.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

rewrite24.0ms (1%)

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:

8.0ms	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
5.0ms	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
4.0ms	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
3.0ms	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

simplify147.0ms (6.1%)

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

prune138.0ms (5.8%)

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
✓	1.4b	(+.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)))
▶	25.5b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

Compiler

Compiled 4797 to 2463 computations (48.7% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series34.0ms (1.4%)

Counts

2 → 40

Calls

2 calls:

20.0ms	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)
13.0ms	(/.f64 y (exp.f64 z))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

4.0ms	(/.f64 y (exp.f64 z))
0.0ms	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

simplify91.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

667×	`cancel-sign-sub-inv_binary64`
491×	`div-sub_binary64`
379×	`associate-/l*_binary64`
372×	`fma-neg_binary64`
357×	`sub-neg_binary64`

Counts

79 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	95	940
1	212	889
2	532	882
3	1512	871
4	4180	871
5	4619	871
6	5253	871

prune35.0ms (1.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	61	3	64

Error

Counts

64 → 3

Alt Table

Status	Error	Program
✓	1.4b	(+.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)))
✓	25.5b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) x)

Compiler

Compiled 808 to 370 computations (54.2% saved)

regimes179.0ms (7.5%)

Accuracy

Total 0.0b remaining (91.7%)

Threshold costs 0.0b (91.7%)

Counts

34 → 1

Compiler

Compiled 2758 to 1985 computations (28% saved)

simplify3.0ms (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)

sample686.0ms (28.6%)

Algorithm

1×

intervals

Results

401.0ms

8000×

body

128

valid

Compiler

Compiled 72 to 51 computations (29.2% saved)

Details

analyze299.0ms (12.5%)

sample139.0ms (5.8%)

simplify138.0ms (5.8%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series114.0ms (4.8%)

rewrite13.0ms (0.5%)

simplify108.0ms (4.5%)

prune121.0ms (5%)

localize8.0ms (0.4%)

series99.0ms (4.1%)

rewrite24.0ms (1%)

simplify147.0ms (6.1%)

prune138.0ms (5.8%)

localize5.0ms (0.2%)

series34.0ms (1.4%)

rewrite6.0ms (0.2%)

simplify91.0ms (3.8%)

prune35.0ms (1.5%)

regimes179.0ms (7.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample686.0ms (28.6%)

Profiling