Details

analyze1.6s (14%)

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)

sample116.0ms (1%)

Algorithm

1×

intervals

Results

40.0ms	34×	body	2048	valid
23.0ms	174×	body	128	valid
11.0ms	21×	body	1024	valid
10.0ms	13×	body	4096	valid
5.0ms	7×	body	256	valid
3.0ms	7×	body	512	valid
2.0ms	16×	body	128	nan
2.0ms	14×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify402.0ms (3.6%)

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

prune8.0ms (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

28.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	28.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
▶	28.9b	(/.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)

localize30.0ms (0.3%)

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))
✓	0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	1.3b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	19.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series552.0ms (5%)

Counts

4 → 96

Calls

4 calls:

319.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
117.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
88.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
27.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite72.0ms (0.6%)

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:

19.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
16.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
15.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify264.0ms (2.4%)

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

prune392.0ms (3.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	199	8	207
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	199	10	209

Error

4.6b

Counts

209 → 10

Alt Table

Status	Error	Program
▶	28.9b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
	33.1b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	28.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	55.2b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	45.3b	(-.f64 (/.f64 c b) (/.f64 b a))
	45.1b	(/.f64 (neg.f64 b) a)
	41.7b	(neg.f64 (/.f64 c b))
	31.8b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
	45.0b	(.f64 (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) (.f64 a 2))) (sqrt.f64 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b) (*.f64 a 2))))
✓	28.9b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 5609 to 3140 computations (44% saved)

localize31.0ms (0.3%)

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)))))))
	0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
	1.3b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
	19.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series185.0ms (1.7%)

Counts

1 → 20

Calls

1 calls:

185.0ms

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

rewrite45.0ms (0.4%)

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:

28.0ms

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

simplify185.0ms (1.7%)

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

prune440.0ms (4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	254	3	257
Fresh	1	7	8
Picked	0	1	1
Done	1	0	1
Total	256	11	267

Error

4.6b

Counts

267 → 11

Alt Table

Status	Error	Program
	45.2b	(/.f64 1 (/.f64 (.f64 2 a) (.f64 b -2)))
	45.3b	(-.f64 (/.f64 c b) (/.f64 b a))
✓	28.9b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
	33.1b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
▶	28.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	55.2b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	32.8b	(.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)))))))
	31.8b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
	45.1b	(/.f64 (neg.f64 b) a)
	41.7b	(neg.f64 (/.f64 c b))
	33.3b	(/.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)))))

Compiler

Compiled 7796 to 4567 computations (41.4% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	1.3b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	19.9b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series461.0ms (4.2%)

Counts

4 → 96

Calls

4 calls:

206.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
122.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
104.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
28.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite68.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
17×	`sqrt-prod_binary64`

Counts

4 → 109

Calls

4 calls:

18.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
13.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
5.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))
2.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify393.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

527×	`fma-neg_binary64`
338×	`distribute-rgt-in_binary64`
273×	`cancel-sign-sub-inv_binary64`
155×	`associate-l_binary64`
153×	`associate-r_binary64`

Counts

205 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	5424
1	673	4468
2	2524	4293
3	4550	4293
4	4991	4293
5	4994	4293
6	4884	4293

prune385.0ms (3.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	227	4	231
Fresh	5	4	9
Picked	0	1	1
Done	0	1	1
Total	232	10	242

Error

4.6b

Counts

242 → 10

Alt Table

Status	Error	Program
	36.1b	(/.f64 (.f64 1/2 (+.f64 (.f64 c (.f64 a -4)) 0)) (.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))))
	45.2b	(/.f64 1 (/.f64 (.f64 2 a) (.f64 b -2)))
	45.3b	(-.f64 (/.f64 c b) (/.f64 b a))
	55.2b	(*.f64 (-.f64 b b) (/.f64 1/2 a))
	33.1b	(.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) (/.f64 1/2 a))
✓	28.9b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
	41.7b	(neg.f64 (/.f64 c b))
✓	28.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	45.2b	(.f64 (.f64 -2 b) (/.f64 1/2 a))
▶	31.8b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))

Compiler

Compiled 6253 to 3660 computations (41.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
✓	0.8b	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
✓	2.5b	(exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)))
✓	12.7b	(sqrt.f64 (.f64 c (.f64 a -4)))

series1.2s (10.5%)

Counts

4 → 36

Calls

4 calls:

438.0ms	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
344.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
335.0ms	(exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)))
51.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite46.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
15×	`exp-sum_binary64`
15×	`log-prod_binary64`

Counts

4 → 100

Calls

4 calls:

18.0ms	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
6.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
6.0ms	(exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)))
5.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

simplify140.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

580×	`fma-def_binary64`
348×	`fma-neg_binary64`
342×	`associate-*l/_binary64`
270×	`cancel-sign-sub-inv_binary64`
178×	`associate-/l/_binary64`

Counts

136 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	262	3659
1	564	3335
2	2036	3189
3	4823	3189
4	4892	3189

prune183.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	2	5	7
Picked	1	0	1
Done	1	1	2
Total	185	8	193

Error

2.6b

Counts

193 → 8

Alt Table

Status	Error	Program
	36.1b	(/.f64 (.f64 1/2 (+.f64 (.f64 c (.f64 a -4)) 0)) (.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))))
	45.2b	(/.f64 1 (/.f64 (.f64 2 a) (.f64 b -2)))
	33.1b	(.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) (/.f64 1/2 a))
	29.5b	(.f64 1/2 (/.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 -4 (*.f64 c a))) b) b) a))
	46.4b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4))) b) b))) (*.f64 2 a))
✓	28.9b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
	41.7b	(neg.f64 (/.f64 c b))
	45.2b	(.f64 (.f64 -2 b) (/.f64 1/2 a))

Compiler

Compiled 5261 to 3458 computations (34.3% saved)

regimes2.0s (18%)

Accuracy

Total 7.2b remaining (69.3%)

Threshold costs 0b (0%)

Counts

149 → 3

Compiler

Compiled 12612 to 8993 computations (28.7% saved)

bsearch62.0ms (0.6%)

Steps

Iters	Range		Point
8	9.058974550953306e-26	3.665883547668106e-21	1.7994370256410445e-25
4	-3.376655171065912e+154	-3.349020245297675e+153	-4.029250158308429e+153

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	50
1	39	50
2	46	50
3	51	50
4	53	50
5	53	50

end1.0ms (0%)

Compiler: Compiled 37 to 25 computations (32.4% saved)

sample1.9s (16.8%)

Algorithm

1×

intervals

Results

443.0ms	5162×	body	128	valid
410.0ms	1171×	body	2048	valid
215.0ms	768×	body	1024	valid
166.0ms	397×	body	4096	valid
69.0ms	327×	body	512	valid
47.0ms	672×	body	128	nan
30.0ms	404×	body	128	invalid
26.0ms	175×	body	256	valid

Compiler

Compiled 199 to 145 computations (27.1% saved)

Details

analyze1.6s (14%)

sample116.0ms (1%)

simplify402.0ms (3.6%)

prune8.0ms (0.1%)

localize30.0ms (0.3%)

series552.0ms (5%)

rewrite72.0ms (0.6%)

simplify264.0ms (2.4%)

prune392.0ms (3.5%)

localize31.0ms (0.3%)

series185.0ms (1.7%)

rewrite45.0ms (0.4%)

simplify185.0ms (1.7%)

prune440.0ms (4%)

localize24.0ms (0.2%)

series461.0ms (4.2%)

rewrite68.0ms (0.6%)

simplify393.0ms (3.5%)

prune385.0ms (3.5%)

localize23.0ms (0.2%)

series1.2s (10.5%)

rewrite46.0ms (0.4%)

simplify140.0ms (1.3%)

prune183.0ms (1.6%)

regimes2.0s (18%)

bsearch62.0ms (0.6%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.9s (16.8%)

Profiling