Details

analyze1.0s (7.8%)

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 (10.7%)

Results

1.0s	8256×	body	128	valid
221.0ms	1865×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify286.0ms (2.1%)

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)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
✓	4.3b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

series49.0ms (0.4%)

Counts

2 → 66

Calls

2 calls:

32.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
17.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

rewrite333.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

1429×	`times-frac_binary64`
1339×	`add-sqr-sqrt_binary64`
1335×	`*-un-lft-identity_binary64`
936×	`prod-diff_binary64`
935×	`add-cube-cbrt_binary64`

Counts

2 → 1074

Calls

2 calls:

41.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
27.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

simplify1.3s (9.8%)

Algorithm

1×	egg-herbie

Rules

687×	`times-frac_binary64`
569×	`associate-l_binary64`
557×	`associate-r_binary64`
314×	`*-commutative_binary64`
243×	`distribute-rgt-in_binary64`

Counts

1140 → 1067

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	990	85623
1	1699	43502
2	3794	41798
3	4686	41798
4	5040	41798

prune1.6s (11.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	1062	5	1067
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1063	5	1068

Error

0.0b

Counts

1068 → 5

Alt Table

Status	Error	Program
	28.3b	(/.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))))
▶	4.4b	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 t) (/.f64 1 (-.f64 1 z)))))
	19.1b	(/.f64 x (/.f64 z (+.f64 y t)))
	10.3b	(+.f64 (.f64 (fma.f64 y (/.f64 1 z) (neg.f64 (.f64 (+.f64 1 z) (/.f64 t (-.f64 (.f64 1 1) (.f64 z z)))))) x) (.f64 (fma.f64 (neg.f64 (+.f64 1 z)) (/.f64 t (-.f64 (.f64 1 1) (.f64 z z))) (.f64 (+.f64 1 z) (/.f64 t (-.f64 (.f64 1 1) (.f64 z z))))) x))
	7.4b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))

Compiler

Compiled 57519 to 31201 computations (45.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 y z) (*.f64 (neg.f64 t) (/.f64 1 (-.f64 1 z))))
✓	0.0b	(/.f64 1 (-.f64 1 z))
✓	0.2b	(*.f64 (neg.f64 t) (/.f64 1 (-.f64 1 z)))
✓	4.3b	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 t) (/.f64 1 (-.f64 1 z)))))

series60.0ms (0.4%)

Counts

4 → 120

Calls

4 calls:

32.0ms	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 t) (/.f64 1 (-.f64 1 z)))))
14.0ms	(+.f64 (/.f64 y z) (*.f64 (neg.f64 t) (/.f64 1 (-.f64 1 z))))
11.0ms	(*.f64 (neg.f64 t) (/.f64 1 (-.f64 1 z)))
2.0ms	(/.f64 1 (-.f64 1 z))

rewrite41.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
47×	`times-frac_binary64`
37×	`add-cube-cbrt_binary64`
27×	`associate-r_binary64`

Counts

4 → 159

Calls

4 calls:

11.0ms	(*.f64 (neg.f64 t) (/.f64 1 (-.f64 1 z)))
9.0ms	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 t) (/.f64 1 (-.f64 1 z)))))
6.0ms	(/.f64 1 (-.f64 1 z))
5.0ms	(+.f64 (/.f64 y z) (*.f64 (neg.f64 t) (/.f64 1 (-.f64 1 z))))

simplify135.0ms (1%)

Algorithm

1×	egg-herbie

Rules

830×	`fma-def_binary64`
380×	`neg-mul-1_binary64`
349×	`fma-neg_binary64`
285×	`times-frac_binary64`
196×	`associate-l_binary64`

Counts

279 → 281

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	244	3958
1	662	3727
2	2273	3696
3	4480	3696
4	5167	3696

prune240.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	280	1	281
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	281	5	286

Error

0.0b

Counts

286 → 5

Alt Table

Status	Error	Program
✓	4.4b	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 t) (/.f64 1 (-.f64 1 z)))))
	19.1b	(/.f64 x (/.f64 z (+.f64 y t)))
	22.4b	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 t) (/.f64 (/.f64 1 (sqrt.f64 (-.f64 1 z))) (sqrt.f64 (-.f64 1 z))))))
	10.3b	(+.f64 (.f64 (fma.f64 y (/.f64 1 z) (neg.f64 (.f64 (+.f64 1 z) (/.f64 t (-.f64 (.f64 1 1) (.f64 z z)))))) x) (.f64 (fma.f64 (neg.f64 (+.f64 1 z)) (/.f64 t (-.f64 (.f64 1 1) (.f64 z z))) (.f64 (+.f64 1 z) (/.f64 t (-.f64 (.f64 1 1) (.f64 z z))))) x))
▶	7.4b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))

Compiler

Compiled 5973 to 3196 computations (46.5% saved)

localize10.0ms (0.1%)

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)))
✓	3.2b	(/.f64 (*.f64 t x) (-.f64 1 z))
✓	7.1b	(/.f64 (*.f64 y x) z)

series60.0ms (0.4%)

Counts

3 → 42

Calls

3 calls:

29.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
19.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
12.0ms	(/.f64 (*.f64 y x) z)

rewrite38.0ms (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:

13.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
5.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
3.0ms	(/.f64 (*.f64 y x) z)

simplify166.0ms (1.2%)

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

prune248.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	251	5	256
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	253	8	261

Error

Counts

261 → 8

Alt Table

Status	Error	Program
	19.1b	(/.f64 x (/.f64 z (+.f64 y t)))
	34.7b	(-.f64 (.f64 (/.f64 y (sqrt.f64 z)) (/.f64 x (sqrt.f64 z))) (/.f64 (.f64 t x) (-.f64 1 z)))
	7.6b	(-.f64 (/.f64 (*.f64 y x) z) (/.f64 t (/.f64 (-.f64 1 z) x)))
	22.4b	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 t) (/.f64 (/.f64 1 (sqrt.f64 (-.f64 1 z))) (sqrt.f64 (-.f64 1 z))))))
	8.8b	(-.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t x) (-.f64 1 z)))
	7.6b	(-.f64 (/.f64 1 (/.f64 z (.f64 y x))) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	4.4b	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 t) (/.f64 1 (-.f64 1 z)))))
▶	7.3b	(-.f64 (/.f64 (.f64 y x) z) (.f64 t (/.f64 x (-.f64 1 z))))

Compiler

Compiled 8416 to 4122 computations (51% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (.f64 y x) z) (.f64 t (/.f64 x (-.f64 1 z))))
✓	3.5b	(*.f64 t (/.f64 x (-.f64 1 z)))
	7.1b	(/.f64 (*.f64 y x) z)

series49.0ms (0.4%)

Counts

2 → 84

Calls

2 calls:

30.0ms	(-.f64 (/.f64 (.f64 y x) z) (.f64 t (/.f64 x (-.f64 1 z))))
19.0ms	(*.f64 t (/.f64 x (-.f64 1 z)))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
24×	`associate-r_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 74

Calls

2 calls:

13.0ms	(*.f64 t (/.f64 x (-.f64 1 z)))
5.0ms	(-.f64 (/.f64 (.f64 y x) z) (.f64 t (/.f64 x (-.f64 1 z))))

simplify92.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

818×	`fma-def_binary64`
387×	`associate-/l*_binary64`
341×	`fma-neg_binary64`
293×	`times-frac_binary64`
181×	`cancel-sign-sub-inv_binary64`

Counts

158 → 149

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	2883
1	509	2763
2	1689	2413
3	4525	2413
4	5146	2413

prune144.0ms (1.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	184	8	192

Error

Counts

192 → 8

Alt Table

Status	Error	Program
	19.1b	(/.f64 x (/.f64 z (+.f64 y t)))
	34.7b	(-.f64 (.f64 (/.f64 y (sqrt.f64 z)) (/.f64 x (sqrt.f64 z))) (/.f64 (.f64 t x) (-.f64 1 z)))
	7.6b	(-.f64 (/.f64 (*.f64 y x) z) (/.f64 t (/.f64 (-.f64 1 z) x)))
	22.4b	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 t) (/.f64 (/.f64 1 (sqrt.f64 (-.f64 1 z))) (sqrt.f64 (-.f64 1 z))))))
	8.8b	(-.f64 (/.f64 y (/.f64 z x)) (/.f64 (*.f64 t x) (-.f64 1 z)))
	7.6b	(-.f64 (/.f64 1 (/.f64 z (.f64 y x))) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	4.4b	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 t) (/.f64 1 (-.f64 1 z)))))
✓	7.3b	(-.f64 (/.f64 (.f64 y x) z) (.f64 t (/.f64 x (-.f64 1 z))))

Compiler

Compiled 3846 to 1664 computations (56.7% saved)

regimes5.9s (44.1%)

Accuracy

Total 0.7b remaining (97.5%)

Threshold costs 0.7b (97.5%)

Counts

348 → 5

Compiler

Compiled 63666 to 42808 computations (32.8% saved)

bsearch17.0ms (0.1%)

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64`
17×	`+-commutative_binary64`
16×	`sub-neg_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	218
1	81	218
2	110	218
3	135	218
4	149	218
5	154	218
6	155	218
7	152	218

end142.0ms (1.1%)

Compiler: Compiled 444 to 269 computations (39.4% saved)

Details

analyze1.0s (7.8%)

sample1.4s (10.7%)

simplify286.0ms (2.1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series49.0ms (0.4%)

rewrite333.0ms (2.5%)

simplify1.3s (9.8%)

prune1.6s (11.6%)

localize9.0ms (0.1%)

series60.0ms (0.4%)

rewrite41.0ms (0.3%)

simplify135.0ms (1%)

prune240.0ms (1.8%)

localize10.0ms (0.1%)

series60.0ms (0.4%)

rewrite38.0ms (0.3%)

simplify166.0ms (1.2%)

prune248.0ms (1.8%)

localize8.0ms (0.1%)

series49.0ms (0.4%)

rewrite23.0ms (0.2%)

simplify92.0ms (0.7%)

prune144.0ms (1.1%)

regimes5.9s (44.1%)

bsearch17.0ms (0.1%)

simplify10.0ms (0.1%)

end142.0ms (1.1%)

Profiling