Details

analyze473.0ms (14.6%)

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
12.5%	87.4%	0.1%	5
12.5%	87.4%	0.1%	6
18.7%	81.1%	0.1%	7
35.9%	64%	0.1%	8
47.2%	52.7%	0.1%	9
52.1%	47.8%	0.1%	10
65.3%	34.5%	0.1%	11
71.4%	28.4%	0.1%	12
74.2%	25.6%	0.1%	13
81.7%	18.1%	0.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.4s (42.7%)

Results

1.3s

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify137.0ms (4.2%)

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
▶	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	4.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 84 to 56 computations (33.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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))
✓	0.2b	(/.f64 -5641895835477563/5000000000000000 y)

series57.0ms (1.8%)

Counts

3 → 72

Calls

3 calls:

43.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
13.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
1.0ms	(/.f64 -5641895835477563/5000000000000000 y)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 68

Calls

3 calls:

2.0ms	(/.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)

simplify74.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

749×	`associate-/l*_binary64`
676×	`associate-/r*_binary64`
402×	`fma-def_binary64`
166×	`distribute-rgt-in_binary64`
153×	`associate-/l/_binary64`

Counts

140 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	224	2754
1	529	2581
2	1700	2532
3	5475	2532

prune83.0ms (2.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	114	3	117

Error

Counts

117 → 3

Alt Table

Status	Error	Program
	26.4b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
▶	0.1b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))))
	4.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 2517 to 1587 computations (36.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series110.0ms (3.4%)

Counts

4 → 46

Calls

4 calls:

48.0ms	(/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y))))
38.0ms	(*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y))
17.0ms	(-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))
6.0ms	(/.f64 (exp.f64 z) y)

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
30×	`add-cube-cbrt_binary64`
28×	`times-frac_binary64`
13×	`associate-r_binary64`

Counts

4 → 114

Calls

4 calls:

5.0ms	(*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y))
4.0ms	(/.f64 (exp.f64 z) y)
3.0ms	(/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y))))
3.0ms	(-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))

simplify116.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

560×	`fma-def_binary64`
295×	`associate-/l/_binary64`
265×	`fma-neg_binary64`
208×	`associate-/r/_binary64`
182×	`distribute-rgt-in_binary64`

Counts

160 → 208

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	286	3371
1	697	3145
2	2237	2976
3	4907	2968
4	5008	2968

prune140.0ms (4.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	208	3	211

Error

Counts

211 → 3

Alt Table

Status	Error	Program
	26.4b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	0.1b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))))
▶	4.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 4604 to 2529 computations (45.1% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 5641895835477563/5000000000000000 (exp.f64 z))
✓	0.6b	(-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))
✓	6.6b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series52.0ms (1.6%)

Counts

3 → 76

Calls

3 calls:

38.0ms

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

11.0ms

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

2.0ms

(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

5.0ms

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

3.0ms

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

3.0ms

(*.f64 5641895835477563/5000000000000000 (exp.f64 z))

simplify85.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

649×	`associate-/r*_binary64`
641×	`fma-def_binary64`
252×	`associate-/r/_binary64`
154×	`associate-/l/_binary64`
129×	`cancel-sign-sub-inv_binary64`

Counts

143 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	2944
1	538	2840
2	1885	2761
3	5021	2761

prune103.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	155	3	158

Error

Counts

158 → 3

Alt Table

Status	Error	Program
▶	26.4b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	0.1b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))))
✓	4.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 3424 to 1749 computations (48.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series30.0ms (0.9%)

Counts

2 → 8

Calls

2 calls:

16.0ms	(*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)))
14.0ms	(/.f64 y (exp.f64 z))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
13×	`associate-r_binary64`

Counts

2 → 63

Calls

2 calls:

5.0ms	(*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)))
3.0ms	(/.f64 y (exp.f64 z))

simplify68.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

849×	`fma-neg_binary64`
708×	`fma-def_binary64`
563×	`cancel-sign-sub-inv_binary64`
433×	`associate-/l/_binary64`
403×	`times-frac_binary64`

Counts

71 → 87

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	116	951
1	275	865
2	716	859
3	1961	841
4	4664	837
5	5021	837

prune47.0ms (1.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	87	3	90

Error

Counts

90 → 3

Alt Table

Status	Error	Program
✓	26.4b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	0.1b	(+.f64 x (/.f64 -1 (-.f64 x (*.f64 5641895835477563/5000000000000000 (/.f64 (exp.f64 z) y)))))
✓	4.0b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 1289 to 583 computations (54.8% saved)

regimes134.0ms (4.1%)

Accuracy

Total 0.0b remaining (92.4%)

Threshold costs 0.0b (92.4%)

Counts

25 → 1

Compiler

Compiled 2055 to 1501 computations (27% 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

end57.0ms (1.8%)

Compiler: Compiled 69 to 49 computations (29% saved)

Details

analyze473.0ms (14.6%)

sample1.4s (42.7%)

simplify137.0ms (4.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series57.0ms (1.8%)

rewrite8.0ms (0.2%)

simplify74.0ms (2.3%)

prune83.0ms (2.6%)

localize8.0ms (0.2%)

series110.0ms (3.4%)

rewrite20.0ms (0.6%)

simplify116.0ms (3.6%)

prune140.0ms (4.3%)

localize8.0ms (0.3%)

series52.0ms (1.6%)

rewrite16.0ms (0.5%)

simplify85.0ms (2.6%)

prune103.0ms (3.2%)

localize6.0ms (0.2%)

series30.0ms (0.9%)

rewrite12.0ms (0.4%)

simplify68.0ms (2.1%)

prune47.0ms (1.4%)

regimes134.0ms (4.1%)

simplify3.0ms (0.1%)

end57.0ms (1.8%)

Profiling