Details

analyze593.0ms (8.6%)

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)

sample206.0ms (3%)

Algorithm

1×

intervals

Results

12.0ms	38×	body	2048	valid
10.0ms	155×	body	128	valid
7.0ms	30×	body	1024	valid
6.0ms	13×	body	4096	valid
3.0ms	14×	body	512	valid
2.0ms	23×	body	128	nan
1.0ms	6×	body	256	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify142.0ms (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 (0.1%)

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

33.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	33.4b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
▶	33.4b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
✓	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	21.4b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series173.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

72.0ms	(/.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))))
42.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
10.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 77

Calls

4 calls:

6.0ms	(/.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)))
0.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

simplify134.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

834×	`times-frac_binary64`
539×	`associate-/l*_binary64`
468×	`fma-def_binary64`
198×	`cancel-sign-sub-inv_binary64`
125×	`associate-/r/_binary64`

Counts

173 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	3876
1	521	3658
2	1578	3494
3	5011	3494

prune159.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	184	9	193
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	186	9	195

Error

3.2b

Counts

195 → 9

Alt Table

Status	Error	Program
	49.0b	(.f64 -1/2 (/.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (sqrt.f64 a)) (sqrt.f64 a)))
	35.9b	(.f64 -1/2 (/.f64 (+.f64 b (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) a))
▶	33.4b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 a (.f64 c -4)) (.f64 b b)))) a))
	47.0b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	34.5b	(.f64 -1/2 (.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) a)))
	36.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	46.9b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	43.8b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 b b (.f64 c (.f64 a -4)))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) a))
	33.5b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))

Compiler

Compiled 5205 to 3143 computations (39.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 a (.f64 c -4)) (*.f64 b b)))) a)
✓	0.8b	(+.f64 (.f64 a (.f64 c -4)) (*.f64 b b))
✓	0.9b	(+.f64 b (sqrt.f64 (+.f64 (.f64 a (.f64 c -4)) (*.f64 b b))))
✓	21.4b	(sqrt.f64 (+.f64 (.f64 a (.f64 c -4)) (*.f64 b b)))

series181.0ms (2.6%)

Counts

4 → 96

Calls

4 calls:

71.0ms	(/.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 a (.f64 c -4)) (*.f64 b b)))) a)
54.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 a (.f64 c -4)) (*.f64 b b))))
44.0ms	(sqrt.f64 (+.f64 (.f64 a (.f64 c -4)) (*.f64 b b)))
10.0ms	(+.f64 (.f64 a (.f64 c -4)) (*.f64 b b))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`

Counts

4 → 83

Calls

4 calls:

9.0ms	(/.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 a (.f64 c -4)) (*.f64 b b)))) a)
6.0ms	(+.f64 b (sqrt.f64 (+.f64 (.f64 a (.f64 c -4)) (*.f64 b b))))
4.0ms	(+.f64 (.f64 a (.f64 c -4)) (*.f64 b b))
4.0ms	(sqrt.f64 (+.f64 (.f64 a (.f64 c -4)) (*.f64 b b)))

simplify120.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

796×	`fma-def_binary64`
456×	`fma-neg_binary64`
312×	`cancel-sign-sub-inv_binary64`
188×	`distribute-rgt-in_binary64`
163×	`distribute-rgt-neg-in_binary64`

Counts

179 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	214	4008
1	600	3826
2	2097	3615
3	4543	3615
4	4958	3615

prune135.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	202	9	211

Error

3.2b

Counts

211 → 9

Alt Table

Status	Error	Program
	34.3b	(.f64 -1/2 (/.f64 (/.f64 (.f64 (.f64 c a) 4) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) a))
	34.5b	(.f64 -1/2 (.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) a)))
	49.0b	(.f64 -1/2 (/.f64 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (sqrt.f64 a)) (sqrt.f64 a)))
	35.9b	(.f64 -1/2 (/.f64 (+.f64 b (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) a))
✓	33.4b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 a (.f64 c -4)) (.f64 b b)))) a))
	47.0b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	36.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	46.9b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
▶	33.5b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))

Compiler

Compiled 5602 to 3405 computations (39.2% saved)

localize11.0ms (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 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 1 a))
	0.9b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	21.4b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series72.0ms (1%)

Counts

1 → 20

Calls

1 calls:

72.0ms

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

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 43

Calls

1 calls:

8.0ms

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

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Rules

460×	`times-frac_binary64`
408×	`associate-l_binary64`
317×	`unswap-sqr_binary64`
311×	`associate-/l*_binary64`
305×	`fma-def_binary64`

Counts

63 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1718
1	370	1571
2	1178	1497
3	4445	1497
4	5276	1497

prune186.0ms (2.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	204	3	207
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	208	8	216

Error

3.2b

Counts

216 → 8

Alt Table

Status	Error	Program
✓	33.4b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 a (.f64 c -4)) (.f64 b b)))) a))
	47.0b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	42.5b	(.f64 -1/2 (/.f64 (.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 1 a)) (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
✓	33.5b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
▶	35.9b	(.f64 -1/2 (/.f64 (+.f64 b (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))) a))
	46.9b	(.f64 -1/2 (.f64 (+.f64 b b) (/.f64 1 a)))
	36.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	42.4b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) a) (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))

Compiler

Compiled 5748 to 3599 computations (37.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))
✓	0.6b	(cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	16.5b	(+.f64 b (.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
	21.4b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series177.0ms (2.6%)

Counts

3 → 92

Calls

3 calls:

60.0ms

(+.f64 b (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))

59.0ms

(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))

58.0ms

(cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`cbrt-prod_binary64`
40×	`add-sqr-sqrt_binary64`
23×	`sqrt-prod_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

3 → 90

Calls

3 calls:

9.0ms

(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))))

2.0ms

(+.f64 b (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))))

1.0ms

(cbrt.f64 (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b))))

simplify175.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

358×	`associate-r_binary64`
259×	`associate-/r*_binary64`
250×	`times-frac_binary64`
245×	`fma-neg_binary64`
237×	`associate-l_binary64`

Counts

182 → 222

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	436	7548
1	1350	7273
2	4922	7273
3	5073	7273

prune585.0ms (8.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	498	1	499
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	499	8	507

Error

3.2b

Counts

507 → 8

Alt Table

Status	Error	Program
✓	33.4b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (+.f64 (.f64 a (.f64 c -4)) (.f64 b b)))) a))
	47.0b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	42.5b	(.f64 -1/2 (/.f64 (.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 1 a)) (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
✓	33.5b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	54.8b	(.f64 -1/2 (/.f64 (+.f64 b (.f64 (exp.f64 (.f64 1/3 (-.f64 (log.f64 (.f64 4 c)) (log.f64 (/.f64 -1 a))))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) a))
	46.9b	(.f64 -1/2 (.f64 (+.f64 b b) (/.f64 1 a)))
	36.7b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	42.4b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) a) (-.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))

Compiler

Compiled 27630 to 17267 computations (37.5% saved)

regimes2.0s (28.3%)

Accuracy

Total 4.4b remaining (44.3%)

Threshold costs 0b (0%)

Counts

146 → 3

Compiler

Compiled 17412 to 11530 computations (33.8% saved)

bsearch36.0ms (0.5%)

Steps

Iters	Range		Point
2	1.7863616746486613e+117	4.696274748892413e+123	1.1867869007991433e+122
6	-1.6634451560823125e-67	-2.9005538505333253e-68	-4.240874875338921e-68

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-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	38	60
2	45	60
3	49	60
4	52	60
5	53	60
6	53	60

end1.0ms (0%)

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

sample1.7s (24.4%)

Algorithm

1×

intervals

Results

378.0ms	1063×	body	2048	valid
350.0ms	5272×	body	128	valid
186.0ms	728×	body	1024	valid
158.0ms	392×	body	4096	valid
72.0ms	378×	body	512	valid
43.0ms	672×	body	128	nan
28.0ms	392×	body	128	invalid
22.0ms	167×	body	256	valid

Compiler

Compiled 250 to 167 computations (33.2% saved)

Details

analyze593.0ms (8.6%)

sample206.0ms (3%)

simplify142.0ms (2.1%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series173.0ms (2.5%)

rewrite14.0ms (0.2%)

simplify134.0ms (1.9%)

prune159.0ms (2.3%)

localize10.0ms (0.1%)

series181.0ms (2.6%)

rewrite27.0ms (0.4%)

simplify120.0ms (1.7%)

prune135.0ms (2%)

localize11.0ms (0.2%)

series72.0ms (1%)

rewrite11.0ms (0.2%)

simplify71.0ms (1%)

prune186.0ms (2.7%)

localize13.0ms (0.2%)

series177.0ms (2.6%)

rewrite21.0ms (0.3%)

simplify175.0ms (2.5%)

prune585.0ms (8.4%)

regimes2.0s (28.3%)

bsearch36.0ms (0.5%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.7s (24.4%)

Profiling