Details

analyze709.0ms (20.7%)

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
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)

sample1.1s (33.1%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify140.0ms (4.1%)

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)))
	2.3b	(+.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)

series67.0ms (2%)

Counts

3 → 72

Calls

3 calls:

54.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
12.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)
1.0ms	(/.f64 -5641895835477563/5000000000000000 y)

rewrite9.0ms (0.3%)

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)

simplify80.0ms (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

prune86.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Error

0.0b

Counts

117 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
▶	2.3b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))
	20.1b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))

Compiler

Compiled 2501 to 1575 computations (37% saved)

localize7.0ms (0.2%)

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))
✓	6.9b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series56.0ms (1.6%)

Counts

3 → 76

Calls

3 calls:

43.0ms

(/.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))

rewrite15.0ms (0.4%)

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

5.0ms

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

3.0ms

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

simplify103.0ms (3%)

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

prune115.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	155	3	158

Error

Counts

158 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
	20.1b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
▶	2.3b	(+.f64 x (.f64 y (/.f64 1 (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 x y)))))

Compiler

Compiled 3442 to 1762 computations (48.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 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))
✓	0.7b	(/.f64 1 (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
✓	6.5b	(.f64 y (/.f64 1 (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 x y))))

series91.0ms (2.6%)

Counts

2 → 72

Calls

2 calls:

47.0ms	(/.f64 1 (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))
44.0ms	(.f64 y (/.f64 1 (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 x y))))

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
19×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`
15×	`associate-r_binary64`

Counts

2 → 75

Calls

2 calls:

9.0ms	(.f64 y (/.f64 1 (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 x y))))
6.0ms	(/.f64 1 (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

simplify148.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

877×	`fma-def_binary64`
385×	`fma-neg_binary64`
271×	`cancel-sign-sub-inv_binary64`
225×	`times-frac_binary64`
188×	`distribute-rgt-neg-in_binary64`

Counts

147 → 160

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	4038
1	648	3837
2	2605	3736
3	4673	3724
4	4986	3724
5	4961	3724

prune209.0ms (6.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	236	3	239

Error

Counts

239 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
▶	20.1b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	2.3b	(+.f64 x (.f64 y (/.f64 1 (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 x y)))))

Compiler

Compiled 5879 to 3274 computations (44.3% saved)

localize7.0ms (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 (0.3%)

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:

7.0ms	(*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)))
3.0ms	(/.f64 y (exp.f64 z))

simplify72.0ms (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

prune48.0ms (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
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	20.1b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	2.3b	(+.f64 x (.f64 y (/.f64 1 (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (*.f64 x y)))))

Compiler

Compiled 1290 to 584 computations (54.7% saved)

regimes197.0ms (5.7%)

Accuracy

Total 0.1b remaining (92%)

Threshold costs 0.1b (92%)

Counts

38 → 1

Compiler

Compiled 3631 to 2540 computations (30% 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

end53.0ms (1.5%)

Compiler: Compiled 70 to 50 computations (28.6% saved)

Details

analyze709.0ms (20.7%)

sample1.1s (33.1%)

simplify140.0ms (4.1%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series67.0ms (2%)

rewrite9.0ms (0.3%)

simplify80.0ms (2.3%)

prune86.0ms (2.5%)

localize7.0ms (0.2%)

series56.0ms (1.6%)

rewrite15.0ms (0.4%)

simplify103.0ms (3%)

prune115.0ms (3.3%)

localize9.0ms (0.3%)

series91.0ms (2.6%)

rewrite20.0ms (0.6%)

simplify148.0ms (4.3%)

prune209.0ms (6.1%)

localize7.0ms (0.2%)

series30.0ms (0.9%)

rewrite12.0ms (0.3%)

simplify72.0ms (2.1%)

prune48.0ms (1.4%)

regimes197.0ms (5.7%)

simplify2.0ms (0.1%)

end53.0ms (1.5%)

Profiling