Details

analyze617.0ms (8.8%)

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)

sample2.7s (39.3%)

Results

824.0ms	1143×	body	2048	valid
641.0ms	5365×	body	128	valid
345.0ms	442×	body	4096	valid
292.0ms	764×	body	1024	valid
121.0ms	1054×	body	128	invalid
103.0ms	350×	body	512	valid
40.0ms	192×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify83.0ms (1.2%)

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

33.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	33.4b	(/.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)

localize8.0ms (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)
✓	0.7b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
✓	1.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	23.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series252.0ms (3.6%)

Counts

4 → 96

Calls

4 calls:

146.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
55.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
41.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
9.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite44.0ms (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)
8.0ms	(-.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))

simplify177.0ms (2.5%)

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

prune262.0ms (3.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	279	13	292
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	280	13	293

Error

5.1b

Counts

293 → 13

Alt Table

Status	Error	Program
	34.5b	(/.f64 (-.f64 (neg.f64 b_2) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))) a)
	44.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) a)) (sqrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	36.5b	(/.f64 (-.f64 (neg.f64 b_2) (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) a)
	45.7b	(exp.f64 (log.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	40.5b	(*.f64 -1/2 (/.f64 c b_2))
	42.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	49.2b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) (sqrt.f64 a)) (sqrt.f64 a))
	38.4b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
▶	31.6b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	33.4b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	56.1b	(/.f64 (-.f64 (neg.f64 b_2) (neg.f64 b_2)) a)
	33.4b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
	42.4b	(/.f64 (*.f64 -2 b_2) a)

Compiler

Compiled 9176 to 2062 computations (77.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	0.6b	(cbrt.f64 a)
✓	0.6b	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
✓	14.4b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series290.0ms (4.1%)

Counts

4 → 38

Calls

4 calls:

155.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
57.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))
40.0ms	(cbrt.f64 a)
37.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
30×	`prod-diff_binary64`
19×	`cbrt-prod_binary64`

Counts

4 → 134

Calls

4 calls:

6.0ms	(-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))
5.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
2.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))
1.0ms	(cbrt.f64 a)

simplify99.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

931×	`times-frac_binary64`
474×	`fma-neg_binary64`
355×	`fma-def_binary64`
300×	`div-sub_binary64`
164×	`unswap-sqr_binary64`

Counts

172 → 181

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	222	3654
1	437	2622
2	1330	2168
3	4158	2159
4	4906	2159

prune104.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	215	2	217
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	219	11	230

Error

0.3b

Counts

230 → 11

Alt Table

Status	Error	Program
	36.5b	(/.f64 (-.f64 (neg.f64 b_2) (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) a)
	47.3b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	34.5b	(/.f64 (-.f64 (neg.f64 b_2) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))) a)
	44.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) a)) (sqrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	46.5b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	40.5b	(*.f64 -1/2 (/.f64 c b_2))
	42.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	49.2b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) (sqrt.f64 a)) (sqrt.f64 a))
	38.4b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
▶	33.4b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	33.4b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))

Compiler

Compiled 7110 to 1576 computations (77.8% saved)

localize27.0ms (0.4%)

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))
	0.7b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
	1.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	23.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series75.0ms (1.1%)

Counts

1 → 20

Calls

1 calls:

75.0ms

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

rewrite16.0ms (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:

12.0ms

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

simplify83.0ms (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

prune217.0ms (3.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	298	1	299
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	299	11	310

Error

0.3b

Counts

310 → 11

Alt Table

Status	Error	Program
	36.5b	(/.f64 (-.f64 (neg.f64 b_2) (expm1.f64 (log1p.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))) a)
	47.3b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	40.0b	(/.f64 (.f64 c a) (.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
✓	33.4b	(.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 a))
	34.5b	(/.f64 (-.f64 (neg.f64 b_2) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))) a)
	44.5b	(.f64 (sqrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2)) a)) (sqrt.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2)) a)))
	46.5b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	40.5b	(*.f64 -1/2 (/.f64 c b_2))
	42.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	38.4b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
▶	33.4b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))

Compiler

Compiled 9644 to 2661 computations (72.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
	0.7b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
	1.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	23.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series77.0ms (1.1%)

Counts

1 → 20

Calls

1 calls:

77.0ms

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

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`times-frac_binary64`
121×	`*-un-lft-identity_binary64`
121×	`add-sqr-sqrt_binary64`
73×	`add-cube-cbrt_binary64`
27×	`associate-/r*_binary64`

Counts

1 → 134

Calls

1 calls:

14.0ms

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

simplify147.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

858×	`times-frac_binary64`
427×	`associate-/l*_binary64`
377×	`fma-neg_binary64`
298×	`fma-def_binary64`
204×	`associate-/r/_binary64`

Counts

154 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	5683
1	445	5239
2	1427	4890
3	4833	4890
4	5033	4890

prune197.0ms (2.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	365	3	368
Fresh	2	7	9
Picked	1	0	1
Done	1	0	1
Total	369	10	379

Error

0.2b

Counts

379 → 10

Alt Table

Status	Error	Program
	38.4b	(/.f64 1 (/.f64 a (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2))))
	46.5b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	47.3b	(/.f64 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 (.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2)) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a))
	40.5b	(*.f64 -1/2 (/.f64 c b_2))
	42.6b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	38.4b	(/.f64 (/.f64 (.f64 c a) (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) a)
	40.0b	(/.f64 (.f64 c a) (.f64 a (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)))
	45.1b	(.f64 (/.f64 1 (/.f64 a (-.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 1 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))))
	34.5b	(/.f64 (-.f64 (neg.f64 b_2) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))) a)
	31.0b	(.f64 1 (/.f64 (-.f64 (neg.f64 b_2) (hypot.f64 b_2 (sqrt.f64 (neg.f64 (.f64 a c))))) a))

Compiler

Compiled 12110 to 2972 computations (75.5% saved)

regimes1.2s (17%)

Accuracy

Total 10.3b remaining (97.7%)

Threshold costs 0b (0%)

Counts

118 → 3

Compiler

Compiled 9295 to 5731 computations (38.3% saved)

bsearch65.0ms (0.9%)

Steps

Iters	Range		Point
8	4.2637395089645743e+45	9.315137461053688e+49	9.1827064063623e+49
6	-5.038317377061348e-44	-8.758004259029913e-45	-1.0888894935980672e-44

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (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	26	53
1	40	53
2	55	53
3	70	53
4	79	53
5	83	53
6	84	53
7	84	53

end128.0ms (1.8%)

Compiler: Compiled 289 to 165 computations (42.9% saved)

Details

analyze617.0ms (8.8%)

sample2.7s (39.3%)

simplify83.0ms (1.2%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series252.0ms (3.6%)

rewrite44.0ms (0.6%)

simplify177.0ms (2.5%)

prune262.0ms (3.8%)

localize11.0ms (0.2%)

series290.0ms (4.1%)

rewrite23.0ms (0.3%)

simplify99.0ms (1.4%)

prune104.0ms (1.5%)

localize27.0ms (0.4%)

series75.0ms (1.1%)

rewrite16.0ms (0.2%)

simplify83.0ms (1.2%)

prune217.0ms (3.1%)

localize10.0ms (0.1%)

series77.0ms (1.1%)

rewrite36.0ms (0.5%)

simplify147.0ms (2.1%)

prune197.0ms (2.8%)

regimes1.2s (17%)

bsearch65.0ms (0.9%)

simplify4.0ms (0.1%)

end128.0ms (1.8%)

Profiling