Details

analyze870.0ms (20.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
13.3%	86.5%	0.2%	9
17.5%	82.3%	0.2%	10
23.6%	75.2%	1.2%	11
25%	72%	2.9%	12
35.8%	59.6%	4.6%	13
40.3%	54.3%	5.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.4s (32.2%)

Results

926.0ms	8256×	body	128	valid
214.0ms	2139×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify66.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-def_binary64`
721×	`fma-neg_binary64`
220×	`cancel-sign-sub-inv_binary64`
144×	`distribute-rgt-in_binary64`
108×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	16	11
2	37	11
3	72	11
4	140	11
5	242	11
6	395	11
7	682	11
8	1049	11
9	1368	11
10	1492	11
11	1530	11
12	1536	11
13	1541	11
14	1541	11
15	1456	11

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

2.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.0b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

Compiler

Compiled 45 to 23 computations (48.9% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.9b	(fma.f64 (/.f64 x y) (-.f64 z t) t)

series20.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

19.0ms

(fma.f64 (/.f64 x y) (-.f64 z t) t)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (/.f64 x y) (-.f64 z t) t)

simplify64.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

550×	`distribute-rgt-neg-out_binary64`
522×	`distribute-lft-neg-out_binary64`
356×	`distribute-rgt-in_binary64`
354×	`distribute-lft-in_binary64`
297×	`times-frac_binary64`

Counts

58 → 23

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	730
1	85	635
2	196	623
3	466	623
4	2285	623
5	4620	623
6	5293	623

prune20.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	20	3	23
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	4	24

Error

0.0b

Counts

24 → 4

Alt Table

Status	Error	Program
	7.3b	(+.f64 (*.f64 x (/.f64 (-.f64 z t) y)) t)
▶	5.1b	(-.f64 (+.f64 t (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
✓	2.0b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
	40.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 (/.f64 x y) (-.f64 z t) t) (fma.f64 (/.f64 x y) (-.f64 z t) t)) (fma.f64 (/.f64 x y) (-.f64 z t) t)))

Compiler

Compiled 388 to 123 computations (68.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 t (/.f64 (*.f64 z x) y))
✓	0.0b	(-.f64 (+.f64 t (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
✓	5.7b	(/.f64 (*.f64 z x) y)
✓	7.1b	(/.f64 (*.f64 t x) y)

series128.0ms (3.1%)

Counts

4 → 24

Calls

4 calls:

87.0ms	(-.f64 (+.f64 t (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
15.0ms	(/.f64 (*.f64 t x) y)
13.0ms	(+.f64 t (/.f64 (*.f64 z x) y))
13.0ms	(/.f64 (*.f64 z x) y)

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
28×	`prod-diff_binary64`
27×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`

Counts

4 → 122

Calls

4 calls:

8.0ms	(-.f64 (+.f64 t (/.f64 (.f64 z x) y)) (/.f64 (.f64 t x) y))
7.0ms	(/.f64 (*.f64 z x) y)
3.0ms	(+.f64 t (/.f64 (*.f64 z x) y))
3.0ms	(/.f64 (*.f64 t x) y)

simplify155.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

931×	`times-frac_binary64`
671×	`fma-def_binary64`
197×	`cancel-sign-sub-inv_binary64`
164×	`fma-neg_binary64`
143×	`distribute-neg-frac_binary64`

Counts

146 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	212	3441
1	538	2208
2	1892	1885
3	4372	1885
4	4956	1885
5	4882	1885

prune105.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	167	4	171
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	169	6	175

Error

Counts

175 → 6

Alt Table

Status	Error	Program
▶	4.0b	(-.f64 (+.f64 t (/.f64 (*.f64 z x) y)) (/.f64 t (/.f64 y x)))
	7.3b	(+.f64 (*.f64 x (/.f64 (-.f64 z t) y)) t)
✓	2.0b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
	4.4b	(-.f64 (+.f64 t (/.f64 z (/.f64 y x))) (/.f64 (*.f64 t x) y))
	38.2b	(/.f64 x (/.f64 y (-.f64 z t)))
	5.2b	(-.f64 (+.f64 t (/.f64 1 (/.f64 y (.f64 z x)))) (/.f64 (.f64 t x) y))

Compiler

Compiled 4186 to 793 computations (81.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 t (/.f64 (*.f64 z x) y))
✓	0.0b	(-.f64 (+.f64 t (/.f64 (*.f64 z x) y)) (/.f64 t (/.f64 y x)))
	5.7b	(/.f64 (*.f64 z x) y)
✓	6.0b	(/.f64 t (/.f64 y x))

series36.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

23.0ms	(-.f64 (+.f64 t (/.f64 (*.f64 z x) y)) (/.f64 t (/.f64 y x)))
13.0ms	(/.f64 t (/.f64 y x))

rewrite81.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

408×	`times-frac_binary64`
359×	`*-un-lft-identity_binary64`
273×	`add-sqr-sqrt_binary64`
264×	`add-cube-cbrt_binary64`
176×	`prod-diff_binary64`

Counts

2 → 318

Calls

2 calls:

19.0ms	(-.f64 (+.f64 t (/.f64 (*.f64 z x) y)) (/.f64 t (/.f64 y x)))
4.0ms	(/.f64 t (/.f64 y x))

simplify301.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-def_binary64`
434×	`associate-*r/_binary64`
369×	`associate-*l/_binary64`
268×	`associate-/r/_binary64`
223×	`associate-/l*_binary64`

Counts

402 → 368

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	579	22782
1	1638	11386
2	4257	11119
3	5026	11119

prune258.0ms (6.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	421	0	421
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	421	6	427

Error

Counts

427 → 6

Alt Table

Status	Error	Program
✓	4.0b	(-.f64 (+.f64 t (/.f64 (*.f64 z x) y)) (/.f64 t (/.f64 y x)))
	7.3b	(+.f64 (*.f64 x (/.f64 (-.f64 z t) y)) t)
✓	2.0b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
▶	4.4b	(-.f64 (+.f64 t (/.f64 z (/.f64 y x))) (/.f64 (*.f64 t x) y))
	38.2b	(/.f64 x (/.f64 y (-.f64 z t)))
	5.2b	(-.f64 (+.f64 t (/.f64 1 (/.f64 y (.f64 z x)))) (/.f64 (.f64 t x) y))

Compiler

Compiled 15622 to 2777 computations (82.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 t (/.f64 z (/.f64 y x)))
✓	0.0b	(-.f64 (+.f64 t (/.f64 z (/.f64 y x))) (/.f64 (*.f64 t x) y))
✓	4.7b	(/.f64 z (/.f64 y x))
	7.1b	(/.f64 (*.f64 t x) y)

series44.0ms (1.1%)

Counts

3 → 132

Calls

3 calls:

20.0ms	(-.f64 (+.f64 t (/.f64 z (/.f64 y x))) (/.f64 (*.f64 t x) y))
12.0ms	(/.f64 z (/.f64 y x))
12.0ms	(+.f64 t (/.f64 z (/.f64 y x)))

rewrite43.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64`
87×	`*-un-lft-identity_binary64`
66×	`add-sqr-sqrt_binary64`
64×	`add-cube-cbrt_binary64`
28×	`prod-diff_binary64`

Counts

3 → 148

Calls

3 calls:

15.0ms	(-.f64 (+.f64 t (/.f64 z (/.f64 y x))) (/.f64 (*.f64 t x) y))
14.0ms	(+.f64 t (/.f64 z (/.f64 y x)))
4.0ms	(/.f64 z (/.f64 y x))

simplify165.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

674×	`fma-def_binary64`
370×	`fma-neg_binary64`
369×	`times-frac_binary64`
312×	`distribute-rgt-in_binary64`
174×	`cancel-sign-sub-inv_binary64`

Counts

280 → 221

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	295	4500
1	683	3912
2	2195	3642
3	4205	3642
4	4929	3642
5	4930	3642

prune145.0ms (3.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	257	0	257
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	257	6	263

Error

Counts

263 → 6

Alt Table

Status	Error	Program
✓	4.0b	(-.f64 (+.f64 t (/.f64 (*.f64 z x) y)) (/.f64 t (/.f64 y x)))
	7.3b	(+.f64 (*.f64 x (/.f64 (-.f64 z t) y)) t)
✓	2.0b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
✓	4.4b	(-.f64 (+.f64 t (/.f64 z (/.f64 y x))) (/.f64 (*.f64 t x) y))
	38.2b	(/.f64 x (/.f64 y (-.f64 z t)))
	5.2b	(-.f64 (+.f64 t (/.f64 1 (/.f64 y (.f64 z x)))) (/.f64 (.f64 t x) y))

Compiler

Compiled 6021 to 1203 computations (80% saved)

regimes157.0ms (3.7%)

Accuracy

Total 2.4b remaining (99.7%)

Threshold costs 0b (0%)

Counts

24 → 3

Compiler

Compiled 2282 to 1312 computations (42.5% saved)

bsearch32.0ms (0.8%)

Steps

Iters	Range		Point
7	7.587147987512453e+130	5.688236276885685e+132	1.0008641094660794e+131
8	-2.369052686826752e+125	-9.174354501033413e+121	-9.356558566033457e+121

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
7×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	55
1	33	55
2	43	55
3	54	55
4	60	55
5	63	55
6	64	55
7	64	55

end81.0ms (1.9%)

Compiler: Compiled 173 to 98 computations (43.4% saved)

Details

analyze870.0ms (20.7%)

sample1.4s (32.2%)

simplify66.0ms (1.6%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series20.0ms (0.5%)

rewrite1.0ms (0%)

simplify64.0ms (1.5%)

prune20.0ms (0.5%)

localize10.0ms (0.2%)

series128.0ms (3.1%)

rewrite30.0ms (0.7%)

simplify155.0ms (3.7%)

prune105.0ms (2.5%)

localize9.0ms (0.2%)

series36.0ms (0.9%)

rewrite81.0ms (1.9%)

simplify301.0ms (7.2%)

prune258.0ms (6.2%)

localize8.0ms (0.2%)

series44.0ms (1.1%)

rewrite43.0ms (1%)

simplify165.0ms (3.9%)

prune145.0ms (3.4%)

regimes157.0ms (3.7%)

bsearch32.0ms (0.8%)

simplify4.0ms (0.1%)

end81.0ms (1.9%)

Profiling