Details

analyze484.0ms (3.7%)

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
25%	74.9%	0.1%	4
37.4%	62.4%	0.1%	5
37.4%	62.4%	0.1%	6
40.6%	54.6%	4.8%	7
48.4%	46%	5.6%	8
53.8%	37.8%	8.3%	9
56.2%	32.6%	11.3%	10
60.8%	26%	13.1%	11
63.8%	21%	15.2%	12
65.1%	17.8%	17%	13
67.7%	13.9%	18.4%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample3.3s (25.4%)

Results

970.0ms	5537×	body	128	valid
736.0ms	1089×	body	2048	valid
396.0ms	397×	body	4096	valid
371.0ms	695×	body	1024	valid
149.0ms	367×	body	512	valid
139.0ms	801×	body	128	invalid
47.0ms	171×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify472.0ms (3.6%)

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

prune3.0ms (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

28.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.2b	(/.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)

localize17.0ms (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)
✓	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	1.0b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series372.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

130.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
129.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
95.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
17.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite134.0ms (1%)

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:

13.0ms	(/.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))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
3.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify487.0ms (3.7%)

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	8791
1	779	6792
2	2682	5750
3	4584	5750
4	4974	5750

prune349.0ms (2.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	284	8	292
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	284	9	293

Error

4.1b

Counts

293 → 9

Alt Table

Status	Error	Program
	42.2b	(/.f64 (*.f64 -2 b_2) a)
✓	28.2b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
	28.6b	(/.f64 (.f64 (cbrt.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))) (cbrt.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) (/.f64 a (cbrt.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))))
	46.3b	(/.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 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
▶	28.3b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	29.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
	41.5b	(*.f64 -1/2 (/.f64 c b_2))
	42.3b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	34.1b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)

Compiler

Compiled 9070 to 1968 computations (78.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	1.0b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
	24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series158.0ms (1.2%)

Counts

1 → 20

Calls

1 calls:

158.0ms

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

rewrite20.0ms (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:

16.0ms

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

simplify160.0ms (1.2%)

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

prune338.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	298	1	299
Fresh	2	5	7
Picked	0	1	1
Done	1	0	1
Total	301	7	308

Error

4.1b

Counts

308 → 7

Alt Table

Status	Error	Program
	41.5b	(*.f64 -1/2 (/.f64 c b_2))
	36.3b	(/.f64 (.f64 c a) (.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	42.2b	(/.f64 (*.f64 -2 b_2) a)
✓	28.3b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
▶	29.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
	42.3b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	34.1b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)

Compiler

Compiled 9416 to 2545 computations (73% saved)

localize12.0ms (0.1%)

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))
✓	12.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series1.3s (10%)

Counts

4 → 42

Calls

4 calls:

622.0ms	(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
341.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
278.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
67.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite60.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

172×	`*-un-lft-identity_binary64`
162×	`times-frac_binary64`
139×	`add-sqr-sqrt_binary64`
104×	`add-cube-cbrt_binary64`
34×	`distribute-lft-out--_binary64`

Counts

4 → 244

Calls

4 calls:

11.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))))
8.0ms	(/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)))
7.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
1.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify449.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

715×	`fma-def_binary64`
401×	`fma-neg_binary64`
316×	`cancel-sign-sub-inv_binary64`
186×	`sub-neg_binary64`
154×	`distribute-frac-neg_binary64`

Counts

286 → 331

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	349	9712
1	794	8164
2	2705	7612
3	4798	7608
4	4906	7608

prune355.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	328	3	331
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	330	8	338

Error

0.3b

Counts

338 → 8

Alt Table

Status	Error	Program
	41.5b	(*.f64 -1/2 (/.f64 c b_2))
	36.3b	(/.f64 (.f64 c a) (.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
▶	34.1b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	48.0b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
	41.4b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))
✓	28.3b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	42.3b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	45.6b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))

Compiler

Compiled 10393 to 2636 computations (74.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
✓	2.3b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
✓	6.6b	(/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))
	12.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series1.6s (12%)

Counts

3 → 36

Calls

3 calls:

674.0ms

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

603.0ms

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

288.0ms

(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)

rewrite56.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
47×	`add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 125

Calls

3 calls:

15.0ms

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

10.0ms

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

6.0ms

(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)

simplify308.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

720×	`fma-def_binary64`
390×	`cancel-sign-sub-inv_binary64`
251×	`fma-neg_binary64`
247×	`times-frac_binary64`
196×	`associate-/l*_binary64`

Counts

161 → 236

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	5674
1	872	4918
2	3266	4799
3	4807	4797
4	4966	4797
5	4909	4797

prune226.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	255	0	255
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	255	8	263

Error

0.3b

Counts

263 → 8

Alt Table

Status	Error	Program
	41.5b	(*.f64 -1/2 (/.f64 c b_2))
	36.3b	(/.f64 (.f64 c a) (.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
✓	34.1b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	48.0b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2))))
	41.4b	(/.f64 1 (fma.f64 1/2 (/.f64 a b_2) (/.f64 2 (*.f64 (/.f64 c b_2) -1))))
✓	28.3b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	42.3b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	45.6b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2))))

Compiler

Compiled 7405 to 1719 computations (76.8% saved)

regimes2.0s (15.2%)

Accuracy

Total 7.9b remaining (98.8%)

Threshold costs 0b (0%)

Counts

103 → 4

Compiler

Compiled 9143 to 5033 computations (45% saved)

bsearch122.0ms (0.9%)

Steps

Iters	Range	Point
8	4.199021549675812e+120	4.964530208330052e+131	2.4756347151901527e+129
11	-4.03553621741327e-283	1.0650770863787324e-305	-1.148291726482369e-308
8	-2.4259918529072486e+85	-1.9348829176278518e+82	-1.96537383651797e+82

Iters

Range

Point

4.199021549675812e+120

4.964530208330052e+131

2.4756347151901527e+129

-4.03553621741327e-283

1.0650770863787324e-305

-1.148291726482369e-308

-2.4259918529072486e+85

-1.9348829176278518e+82

-1.96537383651797e+82

Compiler

Compiled 4 to 3 computations (25% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	69
1	54	69
2	70	69
3	84	69
4	91	69
5	94	69
6	95	69
7	94	69

end265.0ms (2%)

Compiler: Compiled 226 to 146 computations (35.4% saved)

Details

analyze484.0ms (3.7%)

sample3.3s (25.4%)

simplify472.0ms (3.6%)

prune3.0ms (0%)

localize17.0ms (0.1%)

series372.0ms (2.8%)

rewrite134.0ms (1%)

simplify487.0ms (3.7%)

prune349.0ms (2.7%)

localize14.0ms (0.1%)

series158.0ms (1.2%)

rewrite20.0ms (0.2%)

simplify160.0ms (1.2%)

prune338.0ms (2.6%)

localize12.0ms (0.1%)

series1.3s (10%)

rewrite60.0ms (0.5%)

simplify449.0ms (3.4%)

prune355.0ms (2.7%)

localize9.0ms (0.1%)

series1.6s (12%)

rewrite56.0ms (0.4%)

simplify308.0ms (2.4%)

prune226.0ms (1.7%)

regimes2.0s (15.2%)

bsearch122.0ms (0.9%)

simplify9.0ms (0.1%)

end265.0ms (2%)

Profiling