Details

analyze616.0ms (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
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)

sample135.0ms (1.8%)

Algorithm

1×

intervals

Results

12.0ms	32×	body	2048	valid
11.0ms	167×	body	128	valid
6.0ms	16×	body	4096	valid
6.0ms	23×	body	1024	valid
3.0ms	16×	body	512	valid
1.0ms	13×	body	128	nan
1.0ms	11×	body	128	invalid
0.0ms	2×	body	256	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify380.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

2009×	`fma-neg_binary64`
1508×	`div-sub_binary64`
1334×	`associate-/l*_binary64`
1156×	`fma-def_binary64`
685×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	34	22
2	64	22
3	132	22
4	198	22
5	325	22
6	552	22
7	918	22
8	1352	22
9	1554	22
10	2359	22
11	3158	22
12	2565	22
13	2653	22
14	3219	22
15	3361	22
16	3461	22
17	3985	22
18	4171	22
19	4439	22
20	4659	22
21	4701	22
22	4757	22
23	4941	22
24	4941	22
25	3365	22
26	3059	22
27	2983	22
28	2985	22
29	2997	22
30	2997	22
31	2997	22
32	2997	22
33	2736	22

prune4.0ms (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

35.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	35.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
▶	35.8b	(/.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)

localize11.0ms (0.1%)

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))
✓	0.6b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	23.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series442.0ms (5.7%)

Counts

4 → 96

Calls

4 calls:

199.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
185.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
46.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
11.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`fma-def_binary64`
10×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64`

Counts

4 → 90

Calls

4 calls:

9.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
8.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
3.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify121.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-neg_binary64`
327×	`cancel-sign-sub-inv_binary64`
226×	`distribute-rgt-neg-in_binary64`
150×	`distribute-rgt-neg-out_binary64`
146×	`associate-r_binary64`

Counts

186 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	4202
1	693	3825
2	2488	3724
3	4652	3704
4	4985	3704

prune159.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	199	8	207
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	201	8	209

Error

7.9b

Counts

209 → 8

Alt Table

Status	Error	Program
	35.9b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
	38.8b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	35.9b	(.f64 (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) 2) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a))
	40.4b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	37.0b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
	46.1b	(/.f64 (neg.f64 b) a)
	40.1b	(neg.f64 (/.f64 c b))
▶	35.8b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (neg.f64 b)) (.f64 2 a))

Compiler

Compiled 5595 to 3128 computations (44.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (neg.f64 b)) (.f64 2 a))
✓	0.6b	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) (neg.f64 b))
	1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
	23.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series147.0ms (1.9%)

Counts

2 → 40

Calls

2 calls:

93.0ms	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (neg.f64 b)) (.f64 2 a))
54.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) (neg.f64 b))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`distribute-lft-out_binary64`
6×	`add-log-exp_binary64`

Counts

2 → 55

Calls

2 calls:

10.0ms	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (neg.f64 b)) (.f64 2 a))
9.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) (neg.f64 b))

simplify132.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

590×	`fma-def_binary64`
446×	`fma-neg_binary64`
283×	`distribute-rgt-in_binary64`
218×	`distribute-lft-in_binary64`
160×	`cancel-sign-sub-inv_binary64`

Counts

95 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	2627
1	543	2426
2	1895	2313
3	4692	2313
4	4999	2313
5	4992	2313
6	4918	2313

prune136.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	206	8	214

Error

7.9b

Counts

214 → 8

Alt Table

Status	Error	Program
▶	35.9b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
	38.8b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	35.9b	(.f64 (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) 2) (/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a))
	40.4b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	37.0b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
	46.1b	(/.f64 (neg.f64 b) a)
	40.1b	(neg.f64 (/.f64 c b))
✓	35.8b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (neg.f64 b)) (.f64 2 a))

Compiler

Compiled 5581 to 3141 computations (43.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
	0.6b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
	1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
	23.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series125.0ms (1.6%)

Counts

1 → 20

Calls

1 calls:

124.0ms

(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64`
22×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`

Counts

1 → 74

Calls

1 calls:

11.0ms

(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 4 (*.f64 a c)))))))

simplify112.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

665×	`associate-/l*_binary64`
599×	`div-sub_binary64`
346×	`fma-def_binary64`
296×	`fma-neg_binary64`
265×	`associate-/r/_binary64`

Counts

94 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	3247
1	434	2847
2	1512	2670
3	4587	2670
4	6171	2670

prune201.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	254	3	257
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	256	9	265

Error

7.9b

Counts

265 → 9

Alt Table

Status	Error	Program
	38.8b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	46.1b	(/.f64 1 (/.f64 (.f64 2 a) (.f64 b -2)))
▶	37.0b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
	46.1b	(/.f64 (neg.f64 b) a)
	38.8b	(/.f64 1 (/.f64 (.f64 2 a) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b)))))
	40.1b	(neg.f64 (/.f64 c b))
✓	35.8b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (neg.f64 b)) (.f64 2 a))
	37.5b	(.f64 (.f64 (.f64 4 (.f64 c a)) (/.f64 1/2 a)) (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))))
	40.4b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))

Compiler

Compiled 7756 to 4543 computations (41.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 c (.f64 a -4))
✓	0.4b	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
✓	2.6b	(exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)))
✓	15.4b	(sqrt.f64 (.f64 c (.f64 a -4)))

series342.0ms (4.4%)

Counts

4 → 48

Calls

4 calls:

161.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
155.0ms	(exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)))
20.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
5.0ms	(.f64 c (.f64 a -4))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
16×	`pow1_binary64`
15×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`

Counts

4 → 85

Calls

4 calls:

4.0ms	(.f64 c (.f64 a -4))
3.0ms	(exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)))
3.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
3.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

760×	`associate-/l*_binary64`
752×	`fma-def_binary64`
560×	`associate-/r*_binary64`
204×	`fma-neg_binary64`
169×	`cancel-sign-sub-inv_binary64`

Counts

133 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	2456
1	387	2257
2	1340	2184
3	4720	2184
4	5087	2184

prune104.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	134	9	143

Error

5.3b

Counts

143 → 9

Alt Table

Status	Error	Program
	47.8b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b) b))) (*.f64 2 a))
✓	35.8b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (neg.f64 b)) (.f64 2 a))
	38.8b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	46.1b	(/.f64 1 (/.f64 (.f64 2 a) (.f64 b -2)))
	38.0b	(/.f64 (pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (cbrt.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))))) (cbrt.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)))) (.f64 2 a))
	46.1b	(/.f64 (neg.f64 b) a)
	38.8b	(/.f64 1 (/.f64 (.f64 2 a) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b)))))
	40.1b	(neg.f64 (/.f64 c b))
	37.5b	(.f64 (.f64 (.f64 4 (.f64 c a)) (/.f64 1/2 a)) (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))))

Compiler

Compiled 3688 to 2424 computations (34.3% saved)

regimes2.6s (33.5%)

Accuracy

Total 7.2b remaining (68.2%)

Threshold costs 0b (0%)

Counts

172 → 3

Compiler

Compiled 15539 to 11111 computations (28.5% saved)

bsearch72.0ms (0.9%)

Steps

Iters	Range		Point
10	1.1625134004854323e-92	9.387005363483059e-79	1.8003917164795666e-89
8	-2.5495692589417495e+117	-3.525996866042671e+114	-3.738191357919323e+116

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	54
1	38	52
2	46	52
3	54	52
4	59	52
5	62	52
6	63	52
7	63	52

end1.0ms (0%)

Compiler: Compiled 38 to 25 computations (34.2% saved)

sample1.7s (21.7%)

Algorithm

1×

intervals

Results

368.0ms	1134×	body	2048	valid
352.0ms	5234×	body	128	valid
188.0ms	696×	body	1024	valid
167.0ms	425×	body	4096	valid
73.0ms	358×	body	512	valid
45.0ms	668×	body	128	nan
25.0ms	374×	body	128	invalid
19.0ms	153×	body	256	valid

Compiler

Compiled 250 to 180 computations (28% saved)

Details

analyze616.0ms (8%)

sample135.0ms (1.8%)

simplify380.0ms (4.9%)

prune4.0ms (0.1%)

localize11.0ms (0.1%)

series442.0ms (5.7%)

rewrite29.0ms (0.4%)

simplify121.0ms (1.6%)

prune159.0ms (2.1%)

localize12.0ms (0.2%)

series147.0ms (1.9%)

rewrite23.0ms (0.3%)

simplify132.0ms (1.7%)

prune136.0ms (1.8%)

localize12.0ms (0.2%)

series125.0ms (1.6%)

rewrite20.0ms (0.3%)

simplify112.0ms (1.5%)

prune201.0ms (2.6%)

localize11.0ms (0.1%)

series342.0ms (4.4%)

rewrite17.0ms (0.2%)

simplify84.0ms (1.1%)

prune104.0ms (1.4%)

regimes2.6s (33.5%)

bsearch72.0ms (0.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.7s (21.7%)

Profiling