Details

analyze626.0ms (7.5%)

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)

sample2.8s (33.3%)

Results

984.0ms	1182×	body	2048	valid
709.0ms	5349×	body	128	valid
313.0ms	752×	body	1024	valid
298.0ms	419×	body	4096	valid
146.0ms	1165×	body	128	invalid
109.0ms	357×	body	512	valid
43.0ms	197×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify139.0ms (1.7%)

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

prune3.0ms (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

33.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	33.6b	(.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)

localize9.0ms (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)
✓	2.0b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	21.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series148.0ms (1.8%)

Counts

3 → 60

Calls

3 calls:

63.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
46.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
39.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite14.0ms (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:

7.0ms	(/.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)))

simplify99.0ms (1.2%)

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 → 169

Iterations

Useful iterations: 2 (0.0ms)

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

prune139.0ms (1.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	158	11	169
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	158	12	170

Error

3.3b

Counts

170 → 12

Alt Table

Status	Error	Program
	33.9b	(.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (/.f64 a (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))))
	36.8b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	45.1b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
▶	32.2b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	45.6b	(.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))
	34.0b	(.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))) a))
	46.0b	(.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))
	32.2b	(.f64 -1/2 (.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)))
	55.5b	(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
✓	33.6b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	45.2b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	35.0b	(.f64 -1/2 (/.f64 (+.f64 b (.f64 (fabs.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a))

Compiler

Compiled 4840 to 2930 computations (39.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
✓	0.2b	(/.f64 1 (/.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)))))
✓	14.0b	(sqrt.f64 (.f64 a (.f64 c -4)))

series695.0ms (8.3%)

Counts

4 → 42

Calls

4 calls:

339.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
188.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
149.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
19.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 164

Calls

4 calls:

8.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
3.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
3.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))
2.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))

simplify164.0ms (2%)

Algorithm

1×	egg-herbie

Rules

500×	`associate-*l/_binary64`
496×	`fma-def_binary64`
478×	`fma-neg_binary64`
422×	`associate-/r/_binary64`
308×	`cancel-sign-sub-inv_binary64`

Counts

206 → 291

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	6330
1	644	5816
2	2163	5690
3	4938	5684
4	5187	5684

prune262.0ms (3.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	287	4	291
Fresh	4	6	10
Picked	0	1	1
Done	0	1	1
Total	291	12	303

Error

1.7b

Counts

303 → 12

Alt Table

Status	Error	Program
✓	32.2b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	45.6b	(.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))
	32.3b	(.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))) (/.f64 a (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))))
	45.2b	(.f64 -1/2 (/.f64 1 (/.f64 a (.f64 2 b))))
	47.7b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
	34.0b	(.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))) a))
	46.0b	(.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))
▶	32.2b	(.f64 -1/2 (.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)))
	37.1b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (.f64 (/.f64 b (*.f64 -4 c)) -2))))
✓	33.6b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	36.8b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	45.2b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))

Compiler

Compiled 9168 to 6063 computations (33.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))) a))
✓	0.1b	(/.f64 (sqrt.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)))))
	14.0b	(sqrt.f64 (.f64 a (.f64 c -4)))

series640.0ms (7.7%)

Counts

2 → 20

Calls

2 calls:

455.0ms

(/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) a)

185.0ms

(*.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) a))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
50×	`add-sqr-sqrt_binary64`
46×	`times-frac_binary64`
37×	`sqrt-prod_binary64`
34×	`add-cube-cbrt_binary64`

Counts

2 → 105

Calls

2 calls:

12.0ms

(*.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) a))

7.0ms

(/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))) a)

simplify130.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

775×	`times-frac_binary64`
668×	`fma-def_binary64`
654×	`associate-/l*_binary64`
366×	`associate-/r*_binary64`
214×	`associate-/l/_binary64`

Counts

125 → 180

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	4464
1	505	4260
2	1490	4114
3	4783	4114
4	5305	4114

prune310.0ms (3.7%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	318	0	318
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	318	12	330

Error

1.7b

Counts

330 → 12

Alt Table

Status	Error	Program
✓	32.2b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	45.6b	(.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))
▶	32.3b	(.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))) (/.f64 a (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))))
	45.2b	(.f64 -1/2 (/.f64 1 (/.f64 a (.f64 2 b))))
	47.7b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
	34.0b	(.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))) a))
	46.0b	(.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))
✓	32.2b	(.f64 -1/2 (.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)))
	37.1b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (.f64 (/.f64 b (*.f64 -4 c)) -2))))
✓	33.6b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	36.8b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	45.2b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))

Compiler

Compiled 12751 to 8324 computations (34.7% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))
	1.0b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
	14.0b	(sqrt.f64 (.f64 a (.f64 c -4)))
✓	14.0b	(sqrt.f64 (.f64 -4 (.f64 c a)))

series139.0ms (1.7%)

Counts

2 → 14

Calls

2 calls:

121.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))
17.0ms	(sqrt.f64 (.f64 -4 (.f64 c a)))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
3×	`fma-def_binary64`
3×	`sqrt-pow1_binary64`

Counts

2 → 31

Calls

2 calls:

3.0ms	(sqrt.f64 (.f64 -4 (.f64 c a)))
2.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))

simplify53.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

548×	`distribute-rgt-neg-in_binary64`
444×	`times-frac_binary64`
342×	`distribute-neg-frac_binary64`
313×	`associate-r_binary64`
297×	`fma-neg_binary64`

Counts

45 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	880
1	240	826
2	635	810
3	3533	808
4	5380	808

prune119.0ms (1.4%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	123	12	135

Error

1.7b

Counts

135 → 12

Alt Table

Status	Error	Program
✓	32.2b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	45.6b	(.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))
✓	32.3b	(.f64 -1/2 (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))) (/.f64 a (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4)))))))))
	45.2b	(.f64 -1/2 (/.f64 1 (/.f64 a (.f64 2 b))))
	47.7b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
	34.0b	(.f64 -1/2 (/.f64 (exp.f64 (log.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))) a))
	46.0b	(.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))
✓	32.2b	(.f64 -1/2 (.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a)))
	37.1b	(.f64 -1/2 (/.f64 1 (fma.f64 -1/2 (/.f64 a b) (.f64 (/.f64 b (*.f64 -4 c)) -2))))
✓	33.6b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	36.8b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	45.2b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))

Compiler

Compiled 4788 to 3082 computations (35.6% saved)

regimes1.5s (18.3%)

Accuracy

Total 7.8b remaining (74.7%)

Threshold costs 0b (0%)

Counts

119 → 3

Compiler

Compiled 11560 to 8022 computations (30.6% saved)

bsearch60.0ms (0.7%)

Steps

Iters	Range		Point
6	1.853656987300729e+72	2.2780085506493684e+73	2.159988646361628e+73
9	-3.2331823823805678e-139	-4.425920885244571e-148	-3.1847823472437117e-139

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

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	28	60
1	37	60
2	44	60
3	48	60
4	51	60
5	52	60
6	52	60

end167.0ms (2%)

Compiler: Compiled 334 to 231 computations (30.8% saved)

Details

analyze626.0ms (7.5%)

sample2.8s (33.3%)

simplify139.0ms (1.7%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series148.0ms (1.8%)

rewrite14.0ms (0.2%)

simplify99.0ms (1.2%)

prune139.0ms (1.7%)

localize11.0ms (0.1%)

series695.0ms (8.3%)

rewrite32.0ms (0.4%)

simplify164.0ms (2%)

prune262.0ms (3.1%)

localize11.0ms (0.1%)

series640.0ms (7.7%)

rewrite32.0ms (0.4%)

simplify130.0ms (1.6%)

prune310.0ms (3.7%)

localize19.0ms (0.2%)

series139.0ms (1.7%)

rewrite6.0ms (0.1%)

simplify53.0ms (0.6%)

prune119.0ms (1.4%)

regimes1.5s (18.3%)

bsearch60.0ms (0.7%)

simplify4.0ms (0%)

end167.0ms (2%)

Profiling