Details

analyze1.9s (13.6%)

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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample117.0ms (0.9%)

Algorithm

1×

intervals

Results

34.0ms	42×	body	2048	valid
20.0ms	151×	body	128	valid
17.0ms	33×	body	1024	valid
6.0ms	15×	body	512	valid
6.0ms	7×	body	4096	valid
3.0ms	23×	body	128	nan
2.0ms	8×	body	256	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify163.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

2079×	`fma-neg_binary64`
1006×	`fma-def_binary64`
919×	`div-sub_binary64`
626×	`distribute-rgt-in_binary64`
435×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	38	24
2	95	24
3	227	22
4	357	22
5	614	22
6	1103	22
7	1373	22
8	1636	22
9	2330	22
10	3187	22
11	2880	22
12	2827	22
13	2896	22
14	2922	22
15	3797	22
16	4824	22
17	5240	22

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

34.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	34.4b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
▶	34.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	0.5b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	20.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series462.0ms (3.4%)

Counts

4 → 96

Calls

4 calls:

208.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
124.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
100.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
29.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite103.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64`
62×	`*-un-lft-identity_binary64`
61×	`prod-diff_binary64`
50×	`add-cube-cbrt_binary64`
39×	`sqrt-prod_binary64`

Counts

4 → 162

Calls

4 calls:

30.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
17.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
14.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify386.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-neg_binary64`
335×	`cancel-sign-sub-inv_binary64`
185×	`associate-r_binary64`
176×	`unswap-sqr_binary64`
170×	`sub-neg_binary64`

Counts

258 → 277

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	315	7755
1	810	5940
2	2985	5417
3	4824	5409
4	5196	5409

prune558.0ms (4.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	268	9	277
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	270	9	279

Error

3.3b

Counts

279 → 9

Alt Table

Status	Error	Program
	38.5b	(/.f64 (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	32.5b	(/.f64 (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
	44.9b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a 2)) 3))
	47.1b	(-.f64 (/.f64 c b) (/.f64 b a))
	47.0b	(/.f64 (neg.f64 b) a)
▶	32.0b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (*.f64 2 a))
	43.1b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 2 a))
	34.2b	(/.f64 1 (/.f64 (.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
	36.6b	(neg.f64 (/.f64 c b))

Compiler

Compiled 10090 to 5373 computations (46.7% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
✓	1.7b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (*.f64 2 a))
✓	5.2b	(/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))
✓	10.9b	(sqrt.f64 (.f64 c (.f64 a -4)))

series2.6s (19%)

Counts

4 → 36

Calls

4 calls:

1.2s	(/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))
1.0s	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (*.f64 2 a))
307.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
41.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite46.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64`
45×	`add-exp-log_binary64`
28×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`

Counts

4 → 127

Calls

4 calls:

12.0ms	(/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))
9.0ms	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (*.f64 2 a))
4.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
3.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

simplify204.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

479×	`times-frac_binary64`
323×	`fma-neg_binary64`
303×	`associate-/r*_binary64`
300×	`associate-/l*_binary64`
237×	`associate-r_binary64`

Counts

163 → 260

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	344	6012
1	910	4721
2	4222	4697
3	4865	4696
4	4928	4696

prune256.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	260	9	269

Error

3.3b

Counts

269 → 9

Alt Table

Status	Error	Program
	38.5b	(/.f64 (-.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
▶	32.5b	(/.f64 (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
	47.1b	(-.f64 (/.f64 c b) (/.f64 b a))
	47.0b	(/.f64 (neg.f64 b) a)
✓	32.0b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (*.f64 2 a))
	43.1b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 2 a))
	45.1b	(.f64 2 (/.f64 c (sqrt.f64 (.f64 -4 (*.f64 c a)))))
	34.2b	(/.f64 1 (/.f64 (.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
	36.6b	(neg.f64 (/.f64 c b))

Compiler

Compiled 9015 to 5371 computations (40.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)
✓	0.1b	(/.f64 (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
✓	0.3b	(+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))
	10.9b	(sqrt.f64 (.f64 c (.f64 a -4)))

series602.0ms (4.4%)

Counts

3 → 42

Calls

3 calls:

290.0ms	(/.f64 (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
173.0ms	(+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))
138.0ms	(hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`

Counts

3 → 54

Calls

3 calls:

6.0ms	(+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))
5.0ms	(/.f64 (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)) (*.f64 a -2))
0.0ms	(hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)

simplify104.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

913×	`associate-/l*_binary64`
462×	`fma-def_binary64`
257×	`fma-neg_binary64`
204×	`cancel-sign-sub-inv_binary64`
170×	`neg-sub0_binary64`

Counts

96 → 153

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	198	2632
1	569	2413
2	1825	2336
3	4735	2328
4	5033	2328

prune154.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	172	9	181

Error

1.5b

Counts

181 → 9

Alt Table

Status	Error	Program
	47.1b	(-.f64 (/.f64 c b) (/.f64 b a))
▶	32.6b	(/.f64 1 (/.f64 (.f64 a -2) (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))
	38.5b	(/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 a -2))
	47.0b	(/.f64 (neg.f64 b) a)
✓	32.0b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (*.f64 2 a))
	43.1b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 2 a))
	45.1b	(.f64 2 (/.f64 c (sqrt.f64 (.f64 -4 (*.f64 c a)))))
	44.1b	(/.f64 (+.f64 b (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b)) (*.f64 a -2))
	36.6b	(neg.f64 (/.f64 c b))

Compiler

Compiled 4678 to 3012 computations (35.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (.f64 a -2) (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b)))
✓	0.1b	(/.f64 1 (/.f64 (.f64 a -2) (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))
	0.3b	(+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))
	10.9b	(sqrt.f64 (.f64 c (.f64 a -4)))

series689.0ms (5.1%)

Counts

2 → 28

Calls

2 calls:

423.0ms	(/.f64 (.f64 a -2) (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b)))
266.0ms	(/.f64 1 (/.f64 (.f64 a -2) (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
28×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
23×	`add-cube-cbrt_binary64`

Counts

2 → 97

Calls

2 calls:

7.0ms	(/.f64 1 (/.f64 (.f64 a -2) (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))
5.0ms	(/.f64 (.f64 a -2) (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b)))

simplify97.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

730×	`associate-/r*_binary64`
430×	`associate-/r/_binary64`
377×	`fma-def_binary64`
313×	`associate-/l/_binary64`
202×	`distribute-rgt-in_binary64`

Counts

125 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	219	4393
1	597	3857
2	1999	3800
3	5149	3800

prune204.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	252	2	254
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	254	9	263

Error

1.4b

Counts

263 → 9

Alt Table

Status	Error	Program
	47.1b	(-.f64 (/.f64 c b) (/.f64 b a))
✓	32.6b	(/.f64 1 (/.f64 (.f64 a -2) (+.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b))))
	43.1b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 2 a))
	44.1b	(/.f64 1 (/.f64 (.f64 a -2) (+.f64 b (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (*.f64 a -4))) b))))
	38.5b	(/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 a -2))
✓	32.0b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)) (*.f64 2 a))
	45.1b	(.f64 2 (/.f64 c (sqrt.f64 (.f64 -4 (*.f64 c a)))))
	47.1b	(/.f64 1 (neg.f64 (/.f64 a b)))
	36.6b	(neg.f64 (/.f64 c b))

Compiler

Compiled 7367 to 4916 computations (33.3% saved)

regimes2.0s (14.5%)

Accuracy

Total 9.3b remaining (76%)

Threshold costs 0b (0%)

Counts

157 → 3

Compiler

Compiled 14193 to 10038 computations (29.3% saved)

bsearch56.0ms (0.4%)

Steps

Iters	Range		Point
9	2.1844419739613067e+26	5.3939849710379854e+32	9.052048006936924e+27
5	-4.927297779920754e-140	-2.0643786561246256e-140	-4.848123900391362e-140

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	51
1	37	51
2	52	51
3	66	51
4	76	51
5	80	51
6	80	51

end1.0ms (0%)

Compiler: Compiled 37 to 23 computations (37.8% saved)

sample2.9s (21.1%)

Algorithm

1×

intervals

Results

678.0ms	1124×	body	2048	valid
576.0ms	5202×	body	128	valid
367.0ms	762×	body	1024	valid
260.0ms	372×	body	4096	valid
111.0ms	344×	body	512	valid
70.0ms	642×	body	128	nan
44.0ms	396×	body	128	invalid
40.0ms	196×	body	256	valid

Compiler

Compiled 229 to 154 computations (32.8% saved)

Details

analyze1.9s (13.6%)

sample117.0ms (0.9%)

simplify163.0ms (1.2%)

prune7.0ms (0.1%)

localize26.0ms (0.2%)

series462.0ms (3.4%)

rewrite103.0ms (0.8%)

simplify386.0ms (2.8%)

prune558.0ms (4.1%)

localize33.0ms (0.2%)

series2.6s (19%)

rewrite46.0ms (0.3%)

simplify204.0ms (1.5%)

prune256.0ms (1.9%)

localize14.0ms (0.1%)

series602.0ms (4.4%)

rewrite14.0ms (0.1%)

simplify104.0ms (0.8%)

prune154.0ms (1.1%)

localize13.0ms (0.1%)

series689.0ms (5.1%)

rewrite21.0ms (0.2%)

simplify97.0ms (0.7%)

prune204.0ms (1.5%)

regimes2.0s (14.5%)

bsearch56.0ms (0.4%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.9s (21.1%)

Profiling