Details

analyze1.0s (6%)

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
7.8%	92%	0.2%	8
15.6%	84.2%	0.2%	9
23.4%	76.4%	0.2%	10
25%	74.9%	0.2%	11
37.9%	59.6%	2.5%	12
41.4%	55.7%	2.9%	13
46.3%	50.6%	3.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.4s (8.5%)

Results

1.0s	8256×	body	128	valid
220.0ms	1800×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify286.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

2150×	`fma-neg_binary64`
1161×	`div-sub_binary64`
897×	`fma-def_binary64`
414×	`associate-/l*_binary64`
410×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	33	16
3	65	16
4	113	16
5	197	16
6	397	16
7	814	16
8	1449	16
9	1832	16
10	1941	16
11	2036	16
12	2110	16
13	2224	16
14	2174	16
15	2652	16
16	2330	16
17	2358	16
18	2376	16
19	2392	16
20	2384	16
21	2468	16
22	2468	16
23	2388	16
24	2450	16
25	2428	16
26	2426	16
27	2428	16
28	2430	16
29	2440	16
30	2440	16
31	2255	16

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

4.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	4.4b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 1 z))
✓	0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
✓	4.2b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

series62.0ms (0.4%)

Counts

3 → 78

Calls

3 calls:

37.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
14.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
9.0ms	(/.f64 t (-.f64 1 z))

rewrite379.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

1447×	`times-frac_binary64`
1363×	`add-sqr-sqrt_binary64`
1359×	`*-un-lft-identity_binary64`
947×	`add-cube-cbrt_binary64`
936×	`prod-diff_binary64`

Counts

3 → 1117

Calls

3 calls:

39.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
28.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
4.0ms	(/.f64 t (-.f64 1 z))

simplify1.2s (7.1%)

Algorithm

1×	egg-herbie

Rules

854×	`times-frac_binary64`
575×	`associate-l_binary64`
560×	`associate-r_binary64`
316×	`*-commutative_binary64`
254×	`distribute-rgt-in_binary64`

Counts

1195 → 1129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1019	86414
1	1779	44281
2	4035	42577
3	5036	42577

prune1.5s (8.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1122	7	1129
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	1122	8	1130

Error

0.0b

Counts

1130 → 8

Alt Table

Status	Error	Program
✓	4.4b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
	32.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
	32.1b	(*.f64 x (fma.f64 (/.f64 (sqrt.f64 y) 1) (/.f64 (sqrt.f64 y) z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	8.9b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
▶	5.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
	29.3b	(/.f64 (.f64 x (-.f64 (.f64 (/.f64 y z) (/.f64 y z)) (*.f64 (/.f64 t (-.f64 1 z)) (/.f64 t (-.f64 1 z))))) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
	18.3b	(/.f64 x (/.f64 z (+.f64 y t)))
	25.7b	(/.f64 (.f64 x (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t))) (.f64 z (-.f64 1 z)))

Compiler

Compiled 58697 to 31764 computations (45.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	2.2b	(*.f64 (cbrt.f64 x) (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
✓	2.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))

series307.0ms (1.8%)

Counts

4 → 120

Calls

4 calls:

182.0ms	(*.f64 (cbrt.f64 x) (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
53.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
38.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
33.0ms	(cbrt.f64 x)

rewrite1.9s (11%)

Algorithm

1×	rewrite-expression-head

Rules

2816×	`times-frac_binary64`
2644×	`add-sqr-sqrt_binary64`
2631×	`*-un-lft-identity_binary64`
1872×	`prod-diff_binary64`
1864×	`add-cube-cbrt_binary64`

Counts

4 → 2138

Calls

4 calls:

148.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
45.0ms	(*.f64 (cbrt.f64 x) (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
5.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify3.4s (20%)

Algorithm

1×	egg-herbie

Rules

999×	`associate-r_binary64`
996×	`associate-l_binary64`
221×	`fma-udef_binary64`
48×	`neg-mul-1_binary64`
46×	`neg-sub0_binary64`

Counts

2258 → 2896

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2019	184454
1	5558	184454

prune3.0s (17.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	2928	0	2928
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	2928	8	2936

Error

0.0b

Counts

2936 → 8

Alt Table

Status	Error	Program
✓	4.4b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
	32.7b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
	32.1b	(*.f64 x (fma.f64 (/.f64 (sqrt.f64 y) 1) (/.f64 (sqrt.f64 y) z) (neg.f64 (/.f64 t (-.f64 1 z)))))
▶	8.9b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	5.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
	29.3b	(/.f64 (.f64 x (-.f64 (.f64 (/.f64 y z) (/.f64 y z)) (*.f64 (/.f64 t (-.f64 1 z)) (/.f64 t (-.f64 1 z))))) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
	18.3b	(/.f64 x (/.f64 z (+.f64 y t)))
	25.7b	(/.f64 (.f64 x (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t))) (.f64 z (-.f64 1 z)))

Compiler

Compiled 191660 to 91161 computations (52.4% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	3.9b	(/.f64 (*.f64 t x) (-.f64 1 z))
✓	7.3b	(/.f64 (*.f64 y x) z)

series59.0ms (0.4%)

Counts

3 → 42

Calls

3 calls:

29.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
18.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
11.0ms	(/.f64 (*.f64 y x) z)

rewrite47.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64`
84×	`prod-diff_binary64`
81×	`*-un-lft-identity_binary64`
81×	`add-sqr-sqrt_binary64`
49×	`add-cube-cbrt_binary64`

Counts

3 → 173

Calls

3 calls:

14.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
11.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
3.0ms	(/.f64 (*.f64 y x) z)

simplify165.0ms (1%)

Algorithm

1×	egg-herbie

Rules

543×	`fma-neg_binary64`
265×	`cancel-sign-sub-inv_binary64`
213×	`distribute-rgt-neg-in_binary64`
205×	`div-sub_binary64`
190×	`distribute-rgt-out_binary64`

Counts

215 → 256

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	7070
1	799	5494
2	2811	4354
3	4318	4354
4	4944	4354

prune251.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	252	4	256
Fresh	3	2	5
Picked	1	0	1
Done	1	1	2
Total	257	7	264

Error

Counts

264 → 7

Alt Table

Status	Error	Program
✓	4.4b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
	9.1b	(fma.f64 (/.f64 y 1) (/.f64 x z) (neg.f64 (/.f64 (*.f64 t x) (-.f64 1 z))))
	32.1b	(*.f64 x (fma.f64 (/.f64 (sqrt.f64 y) 1) (/.f64 (sqrt.f64 y) z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	9.2b	(-.f64 (/.f64 1 (/.f64 z (.f64 y x))) (/.f64 (.f64 t x) (-.f64 1 z)))
▶	8.7b	(+.f64 (/.f64 (.f64 y x) z) (.f64 (neg.f64 (/.f64 t 1)) (/.f64 x (-.f64 1 z))))
	18.3b	(/.f64 x (/.f64 z (+.f64 y t)))
	9.0b	(-.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t x) (-.f64 1 z)))

Compiler

Compiled 8375 to 4095 computations (51.1% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 1 z))
✓	0.0b	(+.f64 (/.f64 (.f64 y x) z) (.f64 (neg.f64 (/.f64 t 1)) (/.f64 x (-.f64 1 z))))
✓	2.4b	(*.f64 (neg.f64 (/.f64 t 1)) (/.f64 x (-.f64 1 z)))
	7.3b	(/.f64 (*.f64 y x) z)

series69.0ms (0.4%)

Counts

3 → 96

Calls

3 calls:

30.0ms	(*.f64 (neg.f64 (/.f64 t 1)) (/.f64 x (-.f64 1 z)))
29.0ms	(+.f64 (/.f64 (.f64 y x) z) (.f64 (neg.f64 (/.f64 t 1)) (/.f64 x (-.f64 1 z))))
10.0ms	(/.f64 x (-.f64 1 z))

rewrite37.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64`
62×	`*-un-lft-identity_binary64`
58×	`times-frac_binary64`
41×	`add-cube-cbrt_binary64`
30×	`associate-l_binary64`

Counts

3 → 142

Calls

3 calls:

14.0ms	(*.f64 (neg.f64 (/.f64 t 1)) (/.f64 x (-.f64 1 z)))
8.0ms	(/.f64 x (-.f64 1 z))
5.0ms	(+.f64 (/.f64 (.f64 y x) z) (.f64 (neg.f64 (/.f64 t 1)) (/.f64 x (-.f64 1 z))))

simplify122.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

614×	`fma-neg_binary64`
231×	`distribute-lft-neg-out_binary64`
206×	`distribute-rgt-neg-out_binary64`
197×	`distribute-rgt-neg-in_binary64`
193×	`cancel-sign-sub-inv_binary64`

Counts

238 → 262

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	249	3827
1	665	3627
2	2495	3496
3	4506	3494
4	4970	3494

prune229.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	297	7	304

Error

Counts

304 → 7

Alt Table

Status	Error	Program
✓	4.4b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
	9.1b	(fma.f64 (/.f64 y 1) (/.f64 x z) (neg.f64 (/.f64 (*.f64 t x) (-.f64 1 z))))
	32.1b	(*.f64 x (fma.f64 (/.f64 (sqrt.f64 y) 1) (/.f64 (sqrt.f64 y) z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	9.2b	(-.f64 (/.f64 1 (/.f64 z (.f64 y x))) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	8.7b	(+.f64 (/.f64 (.f64 y x) z) (.f64 (neg.f64 (/.f64 t 1)) (/.f64 x (-.f64 1 z))))
	18.3b	(/.f64 x (/.f64 z (+.f64 y t)))
	9.0b	(-.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t x) (-.f64 1 z)))

Compiler

Compiled 6759 to 3371 computations (50.1% saved)

regimes1.3s (7.8%)

Accuracy

Total 2.1b remaining (99.2%)

Threshold costs 0b (0%)

Counts

95 → 4

Compiler

Compiled 14804 to 9583 computations (35.3% saved)

bsearch4.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
9×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	124
1	37	124
2	51	124
3	66	124
4	75	124
5	79	124
6	80	124
7	79	124

end106.0ms (0.6%)

Compiler: Compiled 298 to 176 computations (40.9% saved)

Details

analyze1.0s (6%)

sample1.4s (8.5%)

simplify286.0ms (1.7%)

prune2.0ms (0%)

localize8.0ms (0%)

series62.0ms (0.4%)

rewrite379.0ms (2.2%)

simplify1.2s (7.1%)

prune1.5s (8.9%)

localize12.0ms (0.1%)

series307.0ms (1.8%)

rewrite1.9s (11%)

simplify3.4s (20%)

prune3.0s (17.9%)

localize8.0ms (0%)

series59.0ms (0.4%)

rewrite47.0ms (0.3%)

simplify165.0ms (1%)

prune251.0ms (1.5%)

localize10.0ms (0.1%)

series69.0ms (0.4%)

rewrite37.0ms (0.2%)

simplify122.0ms (0.7%)

prune229.0ms (1.4%)

regimes1.3s (7.8%)

bsearch4.0ms (0%)

simplify8.0ms (0%)

end106.0ms (0.6%)

Profiling