Details

analyze643.0ms (7.8%)

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
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.5s (30.3%)

Results

668.0ms	5362×	body	128	valid
661.0ms	1168×	body	2048	valid
292.0ms	742×	body	1024	valid
259.0ms	447×	body	4096	valid
122.0ms	1033×	body	128	invalid
112.0ms	354×	body	512	valid
38.0ms	183×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify88.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

518×	`div-sub_binary64`
428×	`fma-neg_binary64`
246×	`associate-/l*_binary64`
205×	`fma-def_binary64`
183×	`times-frac_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	27	20
2	54	20
3	115	20
4	179	20
5	291	20
6	417	20
7	528	20
8	602	20
9	854	20
10	1802	20
11	1043	20
12	1027	20
13	1035	20
14	1043	20
15	1043	20
16	1101	20
17	1137	20
18	1139	20
19	1151	20
20	1046	20

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

34.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	34.0b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)

Compiler

Compiled 48 to 30 computations (37.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
✓	1.0b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	22.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series505.0ms (6.2%)

Counts

4 → 96

Calls

4 calls:

308.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
113.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
74.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
9.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite46.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`add-sqr-sqrt_binary64`
80×	`*-un-lft-identity_binary64`
61×	`prod-diff_binary64`
60×	`add-cube-cbrt_binary64`
41×	`sqrt-prod_binary64`

Counts

4 → 176

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
3.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify267.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-neg_binary64`
295×	`cancel-sign-sub-inv_binary64`
181×	`unswap-sqr_binary64`
169×	`sub-neg_binary64`
135×	`associate-r_binary64`

Counts

272 → 292

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	7693
1	779	6304
2	2682	5750
3	4584	5750
4	4974	5750

prune278.0ms (3.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	281	11	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	282	11	293

Error

5.0b

Counts

293 → 11

Alt Table

Status	Error	Program
	36.4b	(/.f64 (-.f64 (neg.f64 b_2) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))) a)
	48.2b	(/.f64 (-.f64 (.f64 (neg.f64 b_2) (neg.f64 b_2)) (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)))
	41.9b	(*.f64 -1/2 (/.f64 c b_2))
	34.1b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	46.5b	(exp.f64 (log.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	43.7b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	31.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
	43.5b	(/.f64 (*.f64 -2 b_2) a)
	33.7b	(/.f64 (-.f64 (neg.f64 b_2) (.f64 (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))) a)
▶	31.0b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
	35.3b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)

Compiler

Compiled 9112 to 2032 computations (77.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
✓	0.5b	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
✓	12.0b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series419.0ms (5.1%)

Counts

3 → 28

Calls

3 calls:

230.0ms	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
167.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
22.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
38×	`add-cube-cbrt_binary64`
30×	`prod-diff_binary64`
18×	`times-frac_binary64`

Counts

3 → 123

Calls

3 calls:

7.0ms	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
7.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
2.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify139.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

526×	`fma-def_binary64`
451×	`fma-neg_binary64`
296×	`div-sub_binary64`
232×	`cancel-sign-sub-inv_binary64`
159×	`distribute-rgt-in_binary64`

Counts

151 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	260	4852
1	599	3789
2	1923	3346
3	4316	3342
4	4897	3342

prune100.0ms (1.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	168	4	172
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	173	10	183

Error

0.0b

Counts

183 → 10

Alt Table

Status	Error	Program
	41.9b	(*.f64 -1/2 (/.f64 c b_2))
	34.1b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	35.3b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	31.1b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (sqrt.f64 (sqrt.f64 (neg.f64 (.f64 c a)))) (sqrt.f64 (sqrt.f64 (neg.f64 (*.f64 c a))))) b_2)) a)
✓	31.0b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
	45.7b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) a)
	46.9b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) a)
▶	31.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
	43.5b	(/.f64 (*.f64 -2 b_2) a)
	48.2b	(/.f64 (-.f64 (.f64 (neg.f64 b_2) (neg.f64 b_2)) (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2))) (.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)))

Compiler

Compiled 5426 to 1292 computations (76.2% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
✓	0.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
	0.5b	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
	12.0b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series626.0ms (7.6%)

Counts

2 → 28

Calls

2 calls:

392.0ms	(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
234.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))

rewrite80.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`times-frac_binary64`
142×	`*-un-lft-identity_binary64`
110×	`add-sqr-sqrt_binary64`
78×	`add-cube-cbrt_binary64`
32×	`distribute-lft-out--_binary64`

Counts

2 → 165

Calls

2 calls:

9.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
6.0ms	(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))

simplify151.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

784×	`associate-/l*_binary64`
391×	`fma-def_binary64`
349×	`associate-/r/_binary64`
175×	`cancel-sign-sub-inv_binary64`
164×	`distribute-rgt-in_binary64`

Counts

193 → 250

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	237	6783
1	596	6192
2	1934	6082
3	5267	6082

prune192.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	351	3	354
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	353	11	364

Error

0.0b

Counts

364 → 11

Alt Table

Status	Error	Program
	41.9b	(*.f64 -1/2 (/.f64 c b_2))
▶	34.1b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	43.5b	(/.f64 (*.f64 -2 b_2) a)
	45.8b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
✓	31.0b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)
	45.7b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) a)
	46.9b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) a)
✓	31.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
	35.3b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	47.0b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))
	44.8b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a c))) b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 a c))) b_2))) a) (+.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))

Compiler

Compiled 11231 to 2786 computations (75.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	1.0b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
	1.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	22.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series89.0ms (1.1%)

Counts

1 → 20

Calls

1 calls:

89.0ms

(*.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 46

Calls

1 calls:

15.0ms

(*.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (*.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Rules

740×	`times-frac_binary64`
400×	`fma-neg_binary64`
392×	`associate-/l*_binary64`
309×	`fma-def_binary64`
212×	`distribute-rgt-in_binary64`

Counts

66 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	1869
1	398	1694
2	1327	1613
3	4987	1613
4	5215	1613

prune150.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	298	1	299
Fresh	2	6	8
Picked	0	1	1
Done	1	1	2
Total	301	9	310

Error

0.0b

Counts

310 → 9

Alt Table

Status	Error	Program
	41.9b	(*.f64 -1/2 (/.f64 c b_2))
✓	34.1b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	43.5b	(/.f64 (*.f64 -2 b_2) a)
	45.8b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
	45.7b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) a)
	46.9b	(/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) a)
✓	31.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
	35.3b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	32.0b	(/.f64 (/.f64 (.f64 c a) a) (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))

Compiler

Compiled 9373 to 2520 computations (73.1% saved)

regimes1.6s (19.4%)

Accuracy

Total 9.5b remaining (98.7%)

Threshold costs 0b (0%)

Counts

113 → 3

Compiler

Compiled 8896 to 5294 computations (40.5% saved)

bsearch52.0ms (0.6%)

Steps

Iters	Range		Point
1	4.823441316663133e+140	5.111513057074458e+140	5.039495121971627e+140
8	-6.220919689581843e-33	-3.0714808753382253e-37	-1.5343846642293365e-36

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	53
1	48	53
2	64	53
3	78	53
4	87	53
5	91	53
6	92	53
7	89	53

end114.0ms (1.4%)

Compiler: Compiled 217 to 141 computations (35% saved)

Details

analyze643.0ms (7.8%)

sample2.5s (30.3%)

simplify88.0ms (1.1%)

prune2.0ms (0%)

localize10.0ms (0.1%)

series505.0ms (6.2%)

rewrite46.0ms (0.6%)

simplify267.0ms (3.3%)

prune278.0ms (3.4%)

localize10.0ms (0.1%)

series419.0ms (5.1%)

rewrite26.0ms (0.3%)

simplify139.0ms (1.7%)

prune100.0ms (1.2%)

localize27.0ms (0.3%)

series626.0ms (7.6%)

rewrite80.0ms (1%)

simplify151.0ms (1.8%)

prune192.0ms (2.3%)

localize11.0ms (0.1%)

series89.0ms (1.1%)

rewrite19.0ms (0.2%)

simplify83.0ms (1%)

prune150.0ms (1.8%)

regimes1.6s (19.4%)

bsearch52.0ms (0.6%)

simplify5.0ms (0.1%)

end114.0ms (1.4%)

Profiling