Details

analyze479.0ms (13%)

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)

sample1.3s (36.4%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify142.0ms (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

prune4.0ms (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)))
	2.8b	(+.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 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))
✓	0.2b	(/.f64 -5641895835477563/5000000000000000 y)

series119.0ms (3.2%)

Counts

4 → 108

Calls

4 calls:

57.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
47.0ms	(/.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)

rewrite14.0ms (0.4%)

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:

5.0ms	(/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x))
4.0ms	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
2.0ms	(/.f64 -5641895835477563/5000000000000000 y)
0.0ms	(fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)

simplify152.0ms (4.1%)

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

prune140.0ms (3.8%)

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
	35.9b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) (fma.f64 25000000000000000000000000000000/31830988618379068626528276418969 (/.f64 (.f64 x (.f64 y y)) (pow.f64 (exp.f64 z) 2)) x))
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
▶	2.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 3793 to 2367 computations (37.6% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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))
✓	7.8b	(/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y)))

series93.0ms (2.5%)

Counts

3 → 108

Calls

3 calls:

42.0ms

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

41.0ms

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

9.0ms

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

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`

Counts

3 → 64

Calls

3 calls:

7.0ms

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

7.0ms

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

4.0ms

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

simplify161.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

825×	`fma-def_binary64`
268×	`fma-neg_binary64`
249×	`associate-/r/_binary64`
223×	`cancel-sign-sub-inv_binary64`
155×	`associate-/l/_binary64`

Counts

172 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	227	4155
1	634	4070
2	2183	3950
3	4734	3940
4	5038	3940

prune129.0ms (3.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	173	3	176

Error

Counts

176 → 3

Alt Table

Status	Error	Program
▶	35.9b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) (fma.f64 25000000000000000000000000000000/31830988618379068626528276418969 (/.f64 (.f64 x (.f64 y y)) (pow.f64 (exp.f64 z) 2)) x))
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	2.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 4232 to 2164 computations (48.9% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 25000000000000000000000000000000/31830988618379068626528276418969 (/.f64 (.f64 x (.f64 y y)) (pow.f64 (exp.f64 z) 2)) x)
✓	0.1b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) (fma.f64 25000000000000000000000000000000/31830988618379068626528276418969 (/.f64 (.f64 x (.f64 y y)) (pow.f64 (exp.f64 z) 2)) x))
✓	6.6b	(/.f64 (.f64 x (.f64 y y)) (pow.f64 (exp.f64 z) 2))
✓	7.3b	(.f64 x (.f64 y y))

series374.0ms (10.1%)

Counts

4 → 132

Calls

4 calls:

142.0ms	(/.f64 (.f64 x (.f64 y y)) (pow.f64 (exp.f64 z) 2))
118.0ms	(fma.f64 25000000000000000000000000000000/31830988618379068626528276418969 (/.f64 (.f64 x (.f64 y y)) (pow.f64 (exp.f64 z) 2)) x)
105.0ms	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) (fma.f64 25000000000000000000000000000000/31830988618379068626528276418969 (/.f64 (.f64 x (.f64 y y)) (pow.f64 (exp.f64 z) 2)) x))
8.0ms	(.f64 x (.f64 y y))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
12×	`prod-exp_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`div-exp_binary64`

Counts

4 → 82

Calls

4 calls:

9.0ms	(/.f64 (.f64 x (.f64 y y)) (pow.f64 (exp.f64 z) 2))
4.0ms	(.f64 x (.f64 y y))
0.0ms	(fma.f64 25000000000000000000000000000000/31830988618379068626528276418969 (/.f64 (.f64 x (.f64 y y)) (pow.f64 (exp.f64 z) 2)) x)
0.0ms	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) (fma.f64 25000000000000000000000000000000/31830988618379068626528276418969 (/.f64 (.f64 x (.f64 y y)) (pow.f64 (exp.f64 z) 2)) x))

simplify108.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

894×	`associate-/l*_binary64`
710×	`fma-def_binary64`
470×	`cancel-sign-sub-inv_binary64`
281×	`associate-/l/_binary64`
206×	`associate-/r/_binary64`

Counts

214 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	195	4277
1	478	3856
2	1754	3789
3	5524	3789

prune114.0ms (3.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	165	3	168

Error

Counts

168 → 3

Alt Table

Status	Error	Program
✓	35.9b	(fma.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)) (fma.f64 25000000000000000000000000000000/31830988618379068626528276418969 (/.f64 (.f64 x (.f64 y y)) (pow.f64 (exp.f64 z) 2)) x))
✓	0.0b	(+.f64 x (/.f64 -1 (fma.f64 (exp.f64 z) (/.f64 -5641895835477563/5000000000000000 y) x)))
✓	2.8b	(+.f64 x (/.f64 y (-.f64 (.f64 5641895835477563/5000000000000000 (exp.f64 z)) (.f64 x y))))

Compiler

Compiled 4283 to 1900 computations (55.6% saved)

regimes176.0ms (4.8%)

Accuracy

Total 0.0b remaining (90.2%)

Threshold costs 0.0b (90.2%)

Counts

30 → 1

Compiler

Compiled 2758 to 1952 computations (29.2% 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

end70.0ms (1.9%)

Compiler: Compiled 79 to 54 computations (31.6% saved)

Details

analyze479.0ms (13%)

sample1.3s (36.4%)

simplify142.0ms (3.9%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series119.0ms (3.2%)

rewrite14.0ms (0.4%)

simplify152.0ms (4.1%)

prune140.0ms (3.8%)

localize10.0ms (0.3%)

series93.0ms (2.5%)

rewrite20.0ms (0.5%)

simplify161.0ms (4.4%)

prune129.0ms (3.5%)

localize13.0ms (0.4%)

series374.0ms (10.1%)

rewrite18.0ms (0.5%)

simplify108.0ms (2.9%)

prune114.0ms (3.1%)

regimes176.0ms (4.8%)

simplify2.0ms (0.1%)

end70.0ms (1.9%)

Profiling