Details

analyze1.3s (9.5%)

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
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)

sample94.0ms (0.7%)

Algorithm

1×

intervals

Results

22.0ms	174×	body	128	valid
22.0ms	34×	body	2048	valid
12.0ms	21×	body	1024	valid
10.0ms	13×	body	4096	valid
3.0ms	7×	body	512	valid
2.0ms	16×	body	128	nan
2.0ms	14×	body	128	invalid
2.0ms	7×	body	256	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify304.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1743×	`fma-neg_binary64`
1393×	`fma-def_binary64`
800×	`div-sub_binary64`
619×	`times-frac_binary64`
473×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	33	22
2	67	22
3	138	22
4	204	22
5	338	22
6	558	22
7	924	22
8	1388	22
9	1604	22
10	2375	22
11	2742	22
12	2533	22
13	2621	22
14	3171	22
15	3313	22
16	3873	22
17	3679	22
18	4029	22
19	4317	22
20	4485	22
21	4561	22
22	4805	22
23	4793	22
24	4797	22
25	4797	22
26	4948	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

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 (.f64 4 a) c)))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize22.0ms (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 (.f64 4 a) c)))) (.f64 2 a))
✓	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	1.3b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	19.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series377.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

167.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
105.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
85.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
20.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite57.0ms (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:

20.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
14.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
6.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify248.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

701×	`fma-neg_binary64`
334×	`cancel-sign-sub-inv_binary64`
215×	`distribute-rgt-neg-in_binary64`
159×	`associate-r_binary64`
150×	`distribute-rgt-neg-out_binary64`

Counts

186 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	4208
1	695	3858
2	2512	3724
3	4694	3704
4	5031	3704

prune319.0ms (2.4%)

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 (.f64 4 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))
	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))
	45.0b	(.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 (.f64 4 a) c)))) (.f64 2 a))
	45.3b	(-.f64 (/.f64 c b) (/.f64 b a))
	45.1b	(/.f64 (neg.f64 b) a)
	55.2b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 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 5609 to 3279 computations (41.5% saved)

localize25.0ms (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 (.f64 4 a) c))))))
	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	1.3b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	19.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series173.0ms (1.3%)

Counts

1 → 20

Calls

1 calls:

173.0ms

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

rewrite54.0ms (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:

25.0ms

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

simplify183.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

94 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	3247
1	439	2847
2	1517	2670
3	4595	2670
4	6178	2670

prune432.0ms (3.2%)

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
✓	28.9b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 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))
	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))
	31.8b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) 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 a (.f64 c -4)))))))
	45.3b	(-.f64 (/.f64 c b) (/.f64 b a))
	45.1b	(/.f64 (neg.f64 b) a)
	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)))))
	55.2b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	45.2b	(/.f64 1 (/.f64 (.f64 2 a) (.f64 b -2)))

Compiler

Compiled 7796 to 4786 computations (38.6% saved)

localize19.0ms (0.1%)

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)))

series379.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

165.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
109.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
88.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
17.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite39.0ms (0.3%)

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:

17.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
7.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
2.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
1.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

simplify315.0ms (2.3%)

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

prune332.0ms (2.5%)

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
	41.7b	(neg.f64 (/.f64 c b))
	45.2b	(.f64 (.f64 -2 b) (/.f64 1/2 a))
✓	28.9b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	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 (.f64 4 a) c))))))
	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)))))))
▶	31.8b	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 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))
	45.2b	(/.f64 1 (/.f64 (.f64 2 a) (.f64 b -2)))

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)))

series1.1s (8%)

Counts

4 → 36

Calls

4 calls:

470.0ms	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
290.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
285.0ms	(exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)))
41.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite51.0ms (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:

15.0ms	(/.f64 (exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b))) (*.f64 2 a))
6.0ms	(exp.f64 (log.f64 (-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)))
6.0ms	(-.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) b)
5.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

simplify209.0ms (1.5%)

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

prune277.0ms (2%)

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

Compiler

Compiled 5261 to 3458 computations (34.3% saved)

regimes3.7s (27.7%)

Accuracy

Total 7.1b remaining (69.1%)

Threshold costs 0b (0%)

Counts

152 → 3

Compiler

Compiled 12812 to 9194 computations (28.2% saved)

bsearch106.0ms (0.8%)

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)

simplify10.0ms (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	25	52
1	39	50
2	50	50
3	56	50
4	58	50
5	58	50

end1.0ms (0%)

Compiler: Compiled 37 to 22 computations (40.5% saved)

sample3.4s (24.8%)

Algorithm

1×

intervals

Results

802.0ms	1171×	body	2048	valid
724.0ms	5162×	body	128	valid
412.0ms	768×	body	1024	valid
325.0ms	397×	body	4096	valid
125.0ms	327×	body	512	valid
89.0ms	672×	body	128	nan
54.0ms	404×	body	128	invalid
45.0ms	175×	body	256	valid

Compiler

Compiled 199 to 142 computations (28.6% saved)

Details

analyze1.3s (9.5%)

sample94.0ms (0.7%)

simplify304.0ms (2.2%)

prune7.0ms (0.1%)

localize22.0ms (0.2%)

series377.0ms (2.8%)

rewrite57.0ms (0.4%)

simplify248.0ms (1.8%)

prune319.0ms (2.4%)

localize25.0ms (0.2%)

series173.0ms (1.3%)

rewrite54.0ms (0.4%)

simplify183.0ms (1.3%)

prune432.0ms (3.2%)

localize19.0ms (0.1%)

series379.0ms (2.8%)

rewrite39.0ms (0.3%)

simplify315.0ms (2.3%)

prune332.0ms (2.5%)

localize23.0ms (0.2%)

series1.1s (8%)

rewrite51.0ms (0.4%)

simplify209.0ms (1.5%)

prune277.0ms (2%)

regimes3.7s (27.7%)

bsearch106.0ms (0.8%)

simplify10.0ms (0.1%)

end1.0ms (0%)

sample3.4s (24.8%)

Profiling