Details

analyze779.0ms (10.3%)

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)

sample54.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms	168×	body	128	valid
13.0ms	39×	body	2048	valid
6.0ms	22×	body	1024	valid
5.0ms	13×	body	4096	valid
1.0ms	7×	body	512	valid
1.0ms	19×	body	128	nan
1.0ms	15×	body	128	invalid
1.0ms	7×	body	256	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify156.0ms (2.1%)

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

prune4.0ms (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

34.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.9b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))

Compiler

Compiled 71 to 46 computations (35.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
✓	1.6b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	23.7b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
5×	`distribute-lft-out_binary64`

Counts

3 → 67

Calls

3 calls:

5.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
3.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series167.0ms (2.2%)

Counts

3 → 60

Calls

3 calls:

69.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
49.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
49.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify486.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

820×	`times-frac_binary64`
539×	`associate-/l*_binary64`
458×	`fma-def_binary64`
246×	`fma-neg_binary64`
189×	`cancel-sign-sub-inv_binary64`

Counts

127 → 232

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	3311
1	510	3170
2	1534	3008
3	4840	3008
4	4954	3008

prune133.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	221	11	232
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	222	11	233

Error

5.8b

Counts

233 → 11

Alt Table

Status	Error	Program
	33.9b	(.f64 -1/2 (.f64 (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))) (cbrt.f64 a))))
	48.6b	(.f64 -1/2 (/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
	49.6b	(.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (.f64 a (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))
	46.9b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
	47.9b	(.f64 -1/2 (/.f64 (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) 3)) (.f64 a (+.f64 (.f64 b b) (-.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))))
	33.4b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	43.0b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
▶	33.4b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))
	40.3b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	43.2b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	56.6b	(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))

Compiler

Compiled 4792 to 2881 computations (39.9% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a)
✓	1.0b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
✓	14.7b	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
9×	`pow1_binary64`

Counts

3 → 66

Calls

3 calls:

4.0ms	(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a)
3.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))
3.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))

series333.0ms (4.4%)

Counts

3 → 28

Calls

3 calls:

185.0ms	(/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))) a)
129.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
18.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

simplify112.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

722×	`associate-/l*_binary64`
598×	`associate-/r*_binary64`
368×	`associate-l_binary64`
333×	`fma-def_binary64`
192×	`associate-*l/_binary64`

Counts

94 → 170

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	2413
1	440	2262
2	1293	2199
3	4963	2199
4	4997	2199

prune128.0ms (1.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	167	3	170
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	169	12	181

Error

2.9b

Counts

181 → 12

Alt Table

Status	Error	Program
	47.9b	(.f64 -1/2 (/.f64 (+.f64 (pow.f64 b 3) (pow.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) 3)) (.f64 a (+.f64 (.f64 b b) (-.f64 (.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))))))
	49.6b	(.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))) (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (.f64 a (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))))
▶	33.4b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	43.0b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
✓	33.4b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))
	40.3b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	43.2b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	48.6b	(.f64 -1/2 (/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
	45.8b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))) a))
	56.6b	(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
	46.9b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
	37.5b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (cbrt.f64 (.f64 (.f64 (sqrt.f64 (.f64 a (.f64 c -4))) (sqrt.f64 (.f64 a (.f64 c -4)))) (sqrt.f64 (.f64 a (*.f64 c -4))))))) a))

Compiler

Compiled 4313 to 2745 computations (36.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
✓	0.1b	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
	1.0b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
	14.7b	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64`
94×	`*-un-lft-identity_binary64`
62×	`add-sqr-sqrt_binary64`
62×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

2 → 133

Calls

2 calls:

7.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
4.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))

series526.0ms (7%)

Counts

2 → 28

Calls

2 calls:

336.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
190.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))

simplify134.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

704×	`associate-/l*_binary64`
646×	`associate-/r*_binary64`
360×	`fma-def_binary64`
321×	`associate-/r/_binary64`
167×	`cancel-sign-sub-inv_binary64`

Counts

161 → 309

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	217	5467
1	542	5019
2	1711	4960
3	5020	4960

prune252.0ms (3.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	387	2	389
Fresh	4	6	10
Picked	0	1	1
Done	0	1	1
Total	391	10	401

Error

2.9b

Counts

401 → 10

Alt Table

Status	Error	Program
	43.2b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	45.4b	(.f64 -1/2 (/.f64 1 (fma.f64 (/.f64 a b) -1/2 (.f64 (/.f64 (.f64 a b) (.f64 -4 (*.f64 a c))) -2))))
	46.9b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
▶	33.5b	(.f64 -1/2 (/.f64 1 (.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))))
✓	33.4b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	43.0b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
✓	33.4b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))
	40.3b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	45.8b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))) a))
	37.5b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (cbrt.f64 (.f64 (.f64 (sqrt.f64 (.f64 a (.f64 c -4))) (sqrt.f64 (.f64 a (.f64 c -4)))) (sqrt.f64 (.f64 a (*.f64 c -4))))))) a))

Compiler

Compiled 9116 to 5980 computations (34.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
✓	0.1b	(.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))
	1.0b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
	14.7b	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
18×	`div-exp_binary64`

Counts

2 → 85

Calls

2 calls:

10.0ms	(.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))
7.0ms	(/.f64 1 (.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))

series525.0ms (6.9%)

Counts

2 → 28

Calls

2 calls:

336.0ms	(.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))
189.0ms	(/.f64 1 (.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))

simplify113.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

696×	`fma-neg_binary64`
329×	`associate-*l/_binary64`
305×	`fma-def_binary64`
285×	`associate-*r/_binary64`
227×	`sub-neg_binary64`

Counts

113 → 211

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	199	3082
1	522	2599
2	1782	2579
3	4002	2575
4	4949	2575

prune197.0ms (2.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	370	1	371
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	370	11	381

Error

2.9b

Counts

381 → 11

Alt Table

Status	Error	Program
	43.0b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	45.9b	(.f64 -1/2 (/.f64 1 (.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (.f64 c -4)))))))))
	43.2b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	45.4b	(.f64 -1/2 (/.f64 1 (fma.f64 (/.f64 a b) -1/2 (.f64 (/.f64 (.f64 a b) (.f64 -4 (*.f64 a c))) -2))))
	46.9b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
✓	33.5b	(.f64 -1/2 (/.f64 1 (.f64 a (/.f64 1 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))))
✓	33.4b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
✓	33.4b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))) a))
	40.3b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	45.8b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))) a))
	37.5b	(.f64 -1/2 (/.f64 (+.f64 b (hypot.f64 b (cbrt.f64 (.f64 (.f64 (sqrt.f64 (.f64 a (.f64 c -4))) (sqrt.f64 (.f64 a (.f64 c -4)))) (sqrt.f64 (.f64 a (*.f64 c -4))))))) a))

Compiler

Compiled 6796 to 4637 computations (31.8% saved)

regimes1.5s (20.2%)

Accuracy

Total 7.9b remaining (72%)

Threshold costs 0b (0%)

Compiler

Compiled 11228 to 7750 computations (31% saved)

bsearch49.0ms (0.7%)

Steps

Iters	Range		Point
6	3.586437907391441e+43	2.682647739852628e+44	2.642290894058981e+44
6	-6.61176354660062e-86	-4.133706132016644e-87	-5.819396861331114e-86

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	60
1	41	60
2	47	60
3	51	60
4	54	60
5	55	60
6	54	60

end1.0ms (0%)

Compiler: Compiled 44 to 29 computations (34.1% saved)

sample1.8s (23.3%)

Algorithm

1×

intervals

Results

393.0ms	1095×	body	2048	valid
370.0ms	5270×	body	128	valid
192.0ms	700×	body	1024	valid
170.0ms	420×	body	4096	valid
72.0ms	352×	body	512	valid
44.0ms	663×	body	128	nan
28.0ms	400×	body	128	invalid
22.0ms	163×	body	256	valid

Compiler

Compiled 284 to 202 computations (28.9% saved)

Details

analyze779.0ms (10.3%)

sample54.0ms (0.7%)

simplify156.0ms (2.1%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite13.0ms (0.2%)

series167.0ms (2.2%)

simplify486.0ms (6.4%)

prune133.0ms (1.8%)

localize9.0ms (0.1%)

rewrite13.0ms (0.2%)

series333.0ms (4.4%)

simplify112.0ms (1.5%)

prune128.0ms (1.7%)

localize10.0ms (0.1%)

rewrite23.0ms (0.3%)

series526.0ms (7%)

simplify134.0ms (1.8%)

prune252.0ms (3.3%)

localize11.0ms (0.2%)

rewrite23.0ms (0.3%)

series525.0ms (6.9%)

simplify113.0ms (1.5%)

prune197.0ms (2.6%)

regimes1.5s (20.2%)

bsearch49.0ms (0.7%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.8s (23.3%)

Profiling