Details

analyze266.0ms (3.9%)

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)

sample1.9s (27.6%)

Results

585.0ms	5562×	body	128	valid
398.0ms	1125×	body	2048	valid
200.0ms	667×	body	1024	valid
161.0ms	372×	body	4096	valid
85.0ms	378×	body	512	valid
69.0ms	717×	body	128	invalid
24.0ms	152×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify305.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-neg_binary64`
379×	`associate-/l*_binary64`
361×	`div-sub_binary64`
341×	`fma-def_binary64`
224×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	23	18
2	39	18
3	69	18
4	107	18
5	178	18
6	279	18
7	382	18
8	547	18
9	587	18
10	855	18
11	1247	18
12	1117	18
13	1035	18
14	1043	18
15	1051	18
16	1077	18
17	1093	18
18	1129	18
19	1131	18
20	1143	18
21	1050	18

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

28.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	28.4b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

Compiler

Compiled 58 to 30 computations (48.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
✓	0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	23.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series227.0ms (3.3%)

Counts

4 → 96

Calls

4 calls:

91.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
75.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
52.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
9.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
20×	`sqrt-prod_binary64`
19×	`prod-diff_binary64`

Counts

4 → 120

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
6.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
3.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
3.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify293.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

682×	`fma-neg_binary64`
364×	`cancel-sign-sub-inv_binary64`
248×	`distribute-rgt-neg-in_binary64`
220×	`distribute-lft-neg-in_binary64`
172×	`distribute-rgt-in_binary64`

Counts

216 → 237

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	5568
1	683	4769
2	2484	4515
3	4521	4514
4	4915	4514
5	4990	4514
6	5000	4514
7	4999	4514
8	4932	4514

prune241.0ms (3.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	226	11	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	227	11	238

Error

5.0b

Counts

238 → 11

Alt Table

Status	Error	Program
▶	28.5b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
	28.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a))) (cbrt.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)))
	29.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (cbrt.f64 a)))
	46.9b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
	41.8b	(/.f64 (-.f64 (cbrt.f64 (pow.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) 3)) b_2) a)
	34.2b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	42.2b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	28.7b	(/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) a)
	42.0b	(*.f64 -1/2 (/.f64 c b_2))
	28.8b	(.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a))
	42.1b	(/.f64 (*.f64 -2 b_2) a)

Compiler

Compiled 5965 to 1716 computations (71.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
	0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	23.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series78.0ms (1.2%)

Counts

1 → 20

Calls

1 calls:

78.0ms

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

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64`
114×	`add-sqr-sqrt_binary64`
90×	`*-un-lft-identity_binary64`
66×	`add-cube-cbrt_binary64`
24×	`associate-/r*_binary64`

Counts

1 → 122

Calls

1 calls:

10.0ms

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

simplify131.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

812×	`fma-def_binary64`
590×	`times-frac_binary64`
369×	`associate-/l*_binary64`
342×	`associate-/r*_binary64`
214×	`associate-*l/_binary64`

Counts

142 → 161

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	5087
1	419	4704
2	1304	4398
3	4392	4398
4	5010	4398

prune225.0ms (3.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	311	2	313
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	315	9	324

Error

5.0b

Counts

324 → 9

Alt Table

Status	Error	Program
✓	28.5b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
	43.8b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) a) (+.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
	29.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (cbrt.f64 a)))
	46.9b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
▶	28.5b	(.f64 (/.f64 1 a) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
	34.2b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	42.2b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	42.0b	(*.f64 -1/2 (/.f64 c b_2))
	42.1b	(/.f64 (*.f64 -2 b_2) a)

Compiler

Compiled 8764 to 2611 computations (70.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 a) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
	0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	23.9b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series107.0ms (1.6%)

Counts

1 → 20

Calls

1 calls:

106.0ms

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

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
36×	`prod-diff_binary64`
35×	`add-cube-cbrt_binary64`
22×	`distribute-lft-in_binary64`

Counts

1 → 88

Calls

1 calls:

12.0ms

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

simplify118.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-def_binary64`
565×	`associate-/l*_binary64`
294×	`fma-neg_binary64`
217×	`distribute-rgt-in_binary64`
196×	`distribute-lft-in_binary64`

Counts

108 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	3181
1	490	2810
2	1619	2487
3	4601	2487
4	4887	2487
5	4851	2487

prune162.0ms (2.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	284	0	284
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	284	9	293

Error

5.0b

Counts

293 → 9

Alt Table

Status	Error	Program
✓	28.5b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
	43.8b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) a) (+.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
▶	29.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (cbrt.f64 a)))
	46.9b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
✓	28.5b	(.f64 (/.f64 1 a) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
	34.2b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	42.2b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	42.0b	(*.f64 -1/2 (/.f64 c b_2))
	42.1b	(/.f64 (*.f64 -2 b_2) a)

Compiler

Compiled 7872 to 2582 computations (67.2% saved)

localize73.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
✓	0.5b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	0.5b	(cbrt.f64 a)
✓	11.8b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series250.0ms (3.7%)

Counts

4 → 36

Calls

4 calls:

154.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
39.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
39.0ms	(cbrt.f64 a)
17.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
19×	`cbrt-prod_binary64`
12×	`pow1_binary64`

Counts

4 → 103

Calls

4 calls:

5.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
3.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
1.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))
1.0ms	(cbrt.f64 a)

simplify103.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary64`
559×	`associate-/l*_binary64`
418×	`associate-/r*_binary64`
233×	`fma-neg_binary64`
200×	`cancel-sign-sub-inv_binary64`

Counts

139 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	193	2143
1	380	1657
2	1267	1554
3	4318	1545
4	4969	1545
5	4879	1545

prune108.0ms (1.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	203	2	205
Fresh	2	4	6
Picked	0	1	1
Done	0	2	2
Total	205	9	214

Error

0.3b

Counts

214 → 9

Alt Table

Status	Error	Program
	44.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 c) (sqrt.f64 (neg.f64 a))) b_2) b_2) (cbrt.f64 a)))
✓	28.5b	(.f64 (/.f64 1 a) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
✓	28.5b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
	43.8b	(/.f64 (/.f64 (-.f64 (.f64 b_2 b_2) (fma.f64 c a (.f64 b_2 b_2))) a) (+.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
✓	29.2b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (cbrt.f64 a)))
	46.9b	(fma.f64 -1/2 (/.f64 c b_2) (.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b_2 3)) -1/8))
	46.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2) (cbrt.f64 a)))
	42.2b	(fma.f64 1/2 (/.f64 c b_2) (*.f64 -2 (/.f64 b_2 a)))
	42.0b	(*.f64 -1/2 (/.f64 c b_2))

Compiler

Compiled 5734 to 1688 computations (70.6% saved)

regimes1.9s (28.1%)

Accuracy

Total 9.0b remaining (97.6%)

Threshold costs 0b (0%)

Counts

128 → 3

Compiler

Compiled 11272 to 6334 computations (43.8% saved)

bsearch53.0ms (0.8%)

Steps

Iters	Range		Point
11	3.4258558715881774e-46	2.6291883852502892e-24	4.8226896466439825e-28
1	-1.0182173360101637e+155	-9.014208010881064e+151	-3.033237869256851e+153

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-commutative_binary64`
9×	`sub-neg_binary64`
8×	`+-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	46
1	40	46
2	53	46
3	64	46
4	72	46
5	76	46
6	77	46
7	76	46

end127.0ms (1.9%)

Compiler: Compiled 239 to 148 computations (38.1% saved)

Details

analyze266.0ms (3.9%)

sample1.9s (27.6%)

simplify305.0ms (4.5%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series227.0ms (3.3%)

rewrite31.0ms (0.5%)

simplify293.0ms (4.3%)

prune241.0ms (3.6%)

localize9.0ms (0.1%)

series78.0ms (1.2%)

rewrite29.0ms (0.4%)

simplify131.0ms (1.9%)

prune225.0ms (3.3%)

localize9.0ms (0.1%)

series107.0ms (1.6%)

rewrite23.0ms (0.3%)

simplify118.0ms (1.7%)

prune162.0ms (2.4%)

localize73.0ms (1.1%)

series250.0ms (3.7%)

rewrite20.0ms (0.3%)

simplify103.0ms (1.5%)

prune108.0ms (1.6%)

regimes1.9s (28.1%)

bsearch53.0ms (0.8%)

simplify4.0ms (0.1%)

end127.0ms (1.9%)

Profiling