Details

analyze1.0s (19.2%)

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
12.5%	87.3%	0.2%	8
18.7%	81.1%	0.2%	9
22.6%	77.2%	0.2%	10
25%	74.9%	0.2%	11
39.4%	60.4%	0.2%	12
46.5%	53.2%	0.3%	13
48%	51.4%	0.6%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.1s (21.3%)

Results

929.0ms	8256×	body	128	valid
109.0ms	724×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1028×	`fma-neg_binary64`
470×	`fma-def_binary64`
271×	`associate-/l*_binary64`
255×	`cancel-sign-sub-inv_binary64`
255×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	24	13
2	53	13
3	109	13
4	185	13
5	336	13
6	549	13
7	870	13
8	1606	13
9	1757	13
10	1912	13
11	1986	13
12	1980	13
13	1985	13
14	1993	13
15	1993	13
16	1872	13

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

4.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	4.9b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
	6.2b	(/.f64 (.f64 x 2) (-.f64 (.f64 y z) (*.f64 t z)))

Compiler

Compiled 80 to 53 computations (33.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (-.f64 y t))
✓	0.2b	(/.f64 (/.f64 2 (-.f64 y t)) z)
✓	4.8b	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))

series79.0ms (1.5%)

Counts

3 → 108

Calls

3 calls:

47.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
22.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
10.0ms	(/.f64 2 (-.f64 y t))

rewrite55.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

249×	`times-frac_binary64`
180×	`add-sqr-sqrt_binary64`
171×	`*-un-lft-identity_binary64`
121×	`add-cube-cbrt_binary64`
67×	`associate-r_binary64`

Counts

3 → 234

Calls

3 calls:

20.0ms	(*.f64 x (/.f64 (/.f64 2 (-.f64 y t)) z))
8.0ms	(/.f64 (/.f64 2 (-.f64 y t)) z)
3.0ms	(/.f64 2 (-.f64 y t))

simplify195.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

292×	`fma-neg_binary64`
246×	`associate-/l*_binary64`
234×	`associate-/r*_binary64`
216×	`times-frac_binary64`
212×	`*-commutative_binary64`

Counts

342 → 351

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	422	7256
1	1123	6896
2	3980	6860
3	4623	6847
4	4989	6847

prune270.0ms (5.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	342	9	351
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	344	9	353

Error

0.0b

Counts

353 → 9

Alt Table

Status	Error	Program
	5.9b	(.f64 (/.f64 x (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (/.f64 2 (-.f64 y t)) (cbrt.f64 z)))
	6.2b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
▶	5.0b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))
	34.2b	(.f64 (.f64 x (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (sqrt.f64 z))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (sqrt.f64 z)))
	32.6b	(.f64 (.f64 x (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (sqrt.f64 (/.f64 2 (-.f64 y t))) (cbrt.f64 z)))
	28.4b	(.f64 (.f64 x (sqrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))) (sqrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z)))
	6.0b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
	5.0b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
	5.2b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) z))

Compiler

Compiled 7669 to 3601 computations (53% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 2 (-.f64 y t))
✓	0.3b	(*.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z))
✓	4.8b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))

series60.0ms (1.1%)

Counts

2 → 84

Calls

2 calls:

39.0ms	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))
21.0ms	(*.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-exp-log_binary64`
42×	`add-sqr-sqrt_binary64`
32×	`add-cbrt-cube_binary64`
31×	`times-frac_binary64`
27×	`*-un-lft-identity_binary64`

Counts

2 → 101

Calls

2 calls:

10.0ms	(*.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z))
8.0ms	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))

simplify87.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-def_binary64`
548×	`associate-/r*_binary64`
191×	`associate-*r/_binary64`
174×	`*-commutative_binary64`
165×	`associate-r_binary64`

Counts

185 → 175

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	3753
1	695	3318
2	2355	3183
3	5082	3183

prune176.0ms (3.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	226	2	228
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	228	9	237

Error

0.0b

Counts

237 → 9

Alt Table

Status	Error	Program
	5.9b	(/.f64 (*.f64 x (/.f64 2 z)) (-.f64 y t))
✓	5.0b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))
	34.2b	(.f64 (.f64 x (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t)))) (sqrt.f64 z))) (/.f64 (/.f64 2 (cbrt.f64 (-.f64 y t))) (sqrt.f64 z)))
	33.9b	(.f64 (/.f64 2 z) (+.f64 (/.f64 x y) (.f64 (/.f64 t (*.f64 y y)) x)))
	28.4b	(.f64 (.f64 x (sqrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))) (sqrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z)))
	6.2b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
	6.0b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 z) (cbrt.f64 z)))) (/.f64 (/.f64 (sqrt.f64 2) (-.f64 y t)) (cbrt.f64 z)))
▶	5.0b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
	5.2b	(.f64 (.f64 x (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 (-.f64 y t)) (cbrt.f64 (-.f64 y t))))) (/.f64 (/.f64 (sqrt.f64 2) (cbrt.f64 (-.f64 y t))) z))

Compiler

Compiled 4808 to 2635 computations (45.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y t) z)
✓	0.0b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
✓	4.9b	(/.f64 x (*.f64 (-.f64 y t) z))

series81.0ms (1.5%)

Counts

3 → 88

Calls

3 calls:

40.0ms	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
34.0ms	(/.f64 x (*.f64 (-.f64 y t) z))
6.0ms	(*.f64 (-.f64 y t) z)

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64`
19×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`

Counts

3 → 80

Calls

3 calls:

7.0ms	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))
7.0ms	(/.f64 x (*.f64 (-.f64 y t) z))
4.0ms	(*.f64 (-.f64 y t) z)

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

880×	`associate-/l*_binary64`
548×	`fma-def_binary64`
214×	`distribute-rgt-in_binary64`
180×	`associate-/r/_binary64`
159×	`distribute-lft-in_binary64`

Counts

168 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	3209
1	493	2822
2	1977	2651
3	5468	2651

prune112.0ms (2.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	157	4	161
Fresh	5	2	7
Picked	0	1	1
Done	0	1	1
Total	162	8	170

Error

Counts

170 → 8

Alt Table

Status	Error	Program
	6.4b	(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (/.f64 x z))))
	6.2b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
▶	4.9b	(.f64 2 (.f64 x (/.f64 (/.f64 1 (-.f64 y t)) z)))
	6.1b	(*.f64 2 (/.f64 1 (/.f64 (-.f64 y t) (/.f64 x z))))
✓	5.0b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))
	32.8b	(.f64 2 (.f64 (/.f64 (sqrt.f64 x) (-.f64 y t)) (/.f64 (sqrt.f64 x) z)))
	28.4b	(.f64 (.f64 x (sqrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))) (sqrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z)))
✓	5.0b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))

Compiler

Compiled 2942 to 1175 computations (60.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 y t))
✓	0.0b	(.f64 2 (.f64 x (/.f64 (/.f64 1 (-.f64 y t)) z)))
✓	0.2b	(/.f64 (/.f64 1 (-.f64 y t)) z)
✓	4.8b	(*.f64 x (/.f64 (/.f64 1 (-.f64 y t)) z))

series117.0ms (2.2%)

Counts

4 → 156

Calls

4 calls:

45.0ms	(*.f64 x (/.f64 (/.f64 1 (-.f64 y t)) z))
44.0ms	(.f64 2 (.f64 x (/.f64 (/.f64 1 (-.f64 y t)) z)))
19.0ms	(/.f64 (/.f64 1 (-.f64 y t)) z)
8.0ms	(/.f64 1 (-.f64 y t))

rewrite66.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`times-frac_binary64`
185×	`add-sqr-sqrt_binary64`
174×	`*-un-lft-identity_binary64`
123×	`add-cube-cbrt_binary64`
68×	`associate-r_binary64`

Counts

4 → 270

Calls

4 calls:

17.0ms	(*.f64 x (/.f64 (/.f64 1 (-.f64 y t)) z))
12.0ms	(.f64 2 (.f64 x (/.f64 (/.f64 1 (-.f64 y t)) z)))
7.0ms	(/.f64 (/.f64 1 (-.f64 y t)) z)
4.0ms	(/.f64 1 (-.f64 y t))

simplify204.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-def_binary64`
232×	`fma-neg_binary64`
223×	`distribute-rgt-in_binary64`
192×	`associate-l_binary64`
190×	`associate-r_binary64`

Counts

426 → 410

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	336	8224
1	851	7526
2	3095	7249
3	4885	7249
4	5004	7249

prune263.0ms (5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	410	0	410
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	410	8	418

Error

Counts

418 → 8

Alt Table

Status	Error	Program
	6.4b	(*.f64 (sqrt.f64 2) (/.f64 (sqrt.f64 2) (/.f64 (-.f64 y t) (/.f64 x z))))
	6.2b	(/.f64 (*.f64 x (/.f64 2 (-.f64 y t))) z)
✓	4.9b	(.f64 2 (.f64 x (/.f64 (/.f64 1 (-.f64 y t)) z)))
	6.1b	(*.f64 2 (/.f64 1 (/.f64 (-.f64 y t) (/.f64 x z))))
✓	5.0b	(.f64 x (.f64 (/.f64 2 (-.f64 y t)) (/.f64 1 z)))
	32.8b	(.f64 2 (.f64 (/.f64 (sqrt.f64 x) (-.f64 y t)) (/.f64 (sqrt.f64 x) z)))
	28.4b	(.f64 (.f64 x (sqrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z))) (sqrt.f64 (/.f64 (/.f64 2 (-.f64 y t)) z)))
✓	5.0b	(.f64 2 (/.f64 x (.f64 (-.f64 y t) z)))

Compiler

Compiled 8859 to 4297 computations (51.5% saved)

regimes1.0s (19.2%)

Accuracy

Total 1.8b remaining (99.2%)

Threshold costs 0b (0%)

Counts

136 → 1

Compiler

Compiled 19006 to 12706 computations (33.1% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	49
1	20	49
2	25	49
3	27	49
4	28	49
5	28	49

end98.0ms (1.9%)

Compiler: Compiled 198 to 132 computations (33.3% saved)

Details

analyze1.0s (19.2%)

sample1.1s (21.3%)

simplify96.0ms (1.8%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series79.0ms (1.5%)

rewrite55.0ms (1%)

simplify195.0ms (3.7%)

prune270.0ms (5.1%)

localize10.0ms (0.2%)

series60.0ms (1.1%)

rewrite30.0ms (0.6%)

simplify87.0ms (1.7%)

prune176.0ms (3.4%)

localize8.0ms (0.1%)

series81.0ms (1.5%)

rewrite22.0ms (0.4%)

simplify71.0ms (1.3%)

prune112.0ms (2.1%)

localize7.0ms (0.1%)

series117.0ms (2.2%)

rewrite66.0ms (1.2%)

simplify204.0ms (3.9%)

prune263.0ms (5%)

regimes1.0s (19.2%)

simplify3.0ms (0.1%)

end98.0ms (1.9%)

Profiling