Details

analyze263.0ms (3.5%)

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 (25.3%)

Infinites

91.5% of outputs are infinite.

Results

549.0ms	5676×	body	128	valid
379.0ms	1026×	body	2048	valid
235.0ms	654×	body	1024	valid
161.0ms	352×	body	4096	valid
90.0ms	381×	body	512	valid
71.0ms	762×	body	128	invalid
27.0ms	167×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify296.0ms (4%)

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

29.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.4b	(/.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)

localize9.0ms (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)
✓	0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
✓	1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
✓	23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series225.0ms (3%)

Counts

4 → 96

Calls

4 calls:

87.0ms	(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)
54.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

rewrite31.0ms (0.4%)

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:

8.0ms	(/.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)
6.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
3.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify273.0ms (3.7%)

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

prune244.0ms (3.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	228	9	237
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	228	10	238

Error

2.8b

Counts

238 → 10

Alt Table

Status	Error	Program
	31.8b	(.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))
	40.7b	(/.f64 (*.f64 -2 b_2) a)
	40.2b	(*.f64 -1/2 (/.f64 c b_2))
	48.4b	(/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (sqrt.f64 a)) (sqrt.f64 a))
	51.1b	(/.f64 (fma.f64 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b_2 5)) -1/16 (fma.f64 (/.f64 (.f64 c a) b_2) -1/2 (.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) -1/8))) a)
	41.4b	(/.f64 (-.f64 (cbrt.f64 (pow.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) 3)) b_2) a)
	37.3b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
	48.4b	(/.f64 (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) (.f64 b_2 b_2)) (.f64 a (+.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))
✓	29.4b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
▶	29.5b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))

Compiler

Compiled 5936 to 1699 computations (71.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
	0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series76.0ms (1%)

Counts

1 → 20

Calls

1 calls:

76.0ms

(/.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:

12.0ms

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

simplify169.0ms (2.3%)

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

prune251.0ms (3.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	312	1	313
Fresh	1	7	8
Picked	0	1	1
Done	1	0	1
Total	314	9	323

Error

2.8b

Counts

323 → 9

Alt Table

Status	Error	Program
	31.8b	(.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))
	40.7b	(/.f64 (*.f64 -2 b_2) a)
	40.2b	(*.f64 -1/2 (/.f64 c b_2))
	48.4b	(/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (sqrt.f64 a)) (sqrt.f64 a))
	51.1b	(/.f64 (fma.f64 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b_2 5)) -1/16 (fma.f64 (/.f64 (.f64 c a) b_2) -1/2 (.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) -1/8))) a)
	41.4b	(/.f64 (-.f64 (cbrt.f64 (pow.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) 3)) b_2) a)
	37.3b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
▶	29.5b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
✓	29.5b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))

Compiler

Compiled 8800 to 2629 computations (70.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
	0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
	1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
	23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series80.0ms (1.1%)

Counts

1 → 20

Calls

1 calls:

79.0ms

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

rewrite113.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

789×	`times-frac_binary64`
484×	`add-sqr-sqrt_binary64`
400×	`*-un-lft-identity_binary64`
316×	`add-cube-cbrt_binary64`
84×	`difference-of-squares_binary64`

Counts

1 → 383

Calls

1 calls:

17.0ms

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

simplify409.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

507×	`associate-/l*_binary64`
362×	`associate-/l/_binary64`
276×	`fma-def_binary64`
274×	`associate-/r/_binary64`
261×	`distribute-rgt-in_binary64`

Counts

403 → 365

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	17318
1	638	16009
2	1977	15019
3	4681	15019
4	5036	15019

prune321.0ms (4.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	516	1	517
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	516	10	526

Error

2.8b

Counts

526 → 10

Alt Table

Status	Error	Program
▶	31.8b	(.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))
	40.7b	(/.f64 (*.f64 -2 b_2) a)
	40.2b	(*.f64 -1/2 (/.f64 c b_2))
	48.4b	(/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (sqrt.f64 a)) (sqrt.f64 a))
	51.1b	(/.f64 (fma.f64 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b_2 5)) -1/16 (fma.f64 (/.f64 (.f64 c a) b_2) -1/2 (.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) -1/8))) a)
	40.8b	(/.f64 (/.f64 1 a) (/.f64 1 (*.f64 b_2 -2)))
	41.4b	(/.f64 (-.f64 (cbrt.f64 (pow.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) 3)) b_2) a)
	37.3b	(/.f64 (-.f64 (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2))) b_2) a)
✓	29.5b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
✓	29.5b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))

Compiler

Compiled 17640 to 6526 computations (63% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
✓	0.2b	(.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))
✓	0.3b	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
✓	11.3b	(sqrt.f64 (neg.f64 (*.f64 c a)))

series904.0ms (12.2%)

Counts

4 → 28

Calls

4 calls:

498.0ms	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
221.0ms	(.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))
165.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
20.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`add-sqr-sqrt_binary64`
65×	`*-un-lft-identity_binary64`
52×	`times-frac_binary64`
51×	`sqrt-prod_binary64`
47×	`add-cube-cbrt_binary64`

Counts

4 → 161

Calls

4 calls:

15.0ms	(.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))
5.0ms	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)) a)
3.0ms	(-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2)
2.0ms	(sqrt.f64 (neg.f64 (*.f64 c a)))

simplify160.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-def_binary64`
337×	`neg-mul-1_binary64`
319×	`fma-neg_binary64`
304×	`cancel-sign-sub-inv_binary64`
165×	`associate-l_binary64`

Counts

189 → 242

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	312	6410
1	698	5446
2	2377	5193
3	4494	5189
4	5013	5189

prune164.0ms (2.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	317	1	318
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	318	10	328

Error

2.8b

Counts

328 → 10

Alt Table

Status	Error	Program
✓	31.8b	(.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))
	40.7b	(/.f64 (*.f64 -2 b_2) a)
	40.2b	(*.f64 -1/2 (/.f64 c b_2))
	48.4b	(/.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) b_2) (sqrt.f64 a)) (sqrt.f64 a))
	51.1b	(/.f64 (fma.f64 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b_2 5)) -1/16 (fma.f64 (/.f64 (.f64 c a) b_2) -1/2 (.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b_2 3)) -1/8))) a)
	40.8b	(/.f64 (/.f64 1 a) (/.f64 1 (*.f64 b_2 -2)))
	41.4b	(/.f64 (-.f64 (cbrt.f64 (pow.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 c a))) b_2) 3)) b_2) a)
	49.7b	(.f64 (sqrt.f64 (-.f64 (hypot.f64 (sqrt.f64 (neg.f64 (.f64 c a))) b_2) b_2)) (/.f64 (sqrt.f64 (-.f64 (hypot.f64 (*.f64 (sqrt.f64 (neg.f64 c)) (sqrt.f64 a)) b_2) b_2)) a))
✓	29.5b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
✓	29.5b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))

Compiler

Compiled 11547 to 2091 computations (81.9% saved)

regimes1.3s (17.2%)

Accuracy

Total 4.6b remaining (48.5%)

Threshold costs 0b (0%)

Counts

119 → 3

Compiler

Compiled 10540 to 6146 computations (41.7% saved)

bsearch42.0ms (0.6%)

Steps

Iters	Range		Point
7	5.1218836308010105e-98	1.850439430127211e-96	1.8313257073812611e-96
6	-2.859172542401454e+165	-2.407018843767758e+164	-2.47012258144473e+164

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	46
1	37	44
2	48	44
3	55	44
4	59	44
5	60	44
6	60	44

end129.0ms (1.7%)

Compiler: Compiled 254 to 161 computations (36.6% saved)

Details

analyze263.0ms (3.5%)

sample1.9s (25.3%)

simplify296.0ms (4%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series225.0ms (3%)

rewrite31.0ms (0.4%)

simplify273.0ms (3.7%)

prune244.0ms (3.3%)

localize9.0ms (0.1%)

series76.0ms (1%)

rewrite29.0ms (0.4%)

simplify169.0ms (2.3%)

prune251.0ms (3.4%)

localize12.0ms (0.2%)

series80.0ms (1.1%)

rewrite113.0ms (1.5%)

simplify409.0ms (5.5%)

prune321.0ms (4.3%)

localize9.0ms (0.1%)

series904.0ms (12.2%)

rewrite43.0ms (0.6%)

simplify160.0ms (2.2%)

prune164.0ms (2.2%)

regimes1.3s (17.2%)

bsearch42.0ms (0.6%)

simplify6.0ms (0.1%)

end129.0ms (1.7%)

Profiling