Details

analyze936.0ms (12.3%)

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)

sample202.0ms (2.7%)

Algorithm

1×

intervals

Results

15.0ms	44×	body	2048	valid
11.0ms	164×	body	128	valid
5.0ms	20×	body	1024	valid
5.0ms	12×	body	4096	valid
2.0ms	12×	body	512	valid
2.0ms	24×	body	128	nan
1.0ms	15×	body	128	invalid
1.0ms	4×	body	256	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify144.0ms (1.9%)

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

35.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	35.1b	(.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 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)
✓	1.0b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	25.5b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series193.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

88.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
51.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
44.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
10.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite13.0ms (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:

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

simplify85.0ms (1.1%)

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

prune144.0ms (1.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	184	9	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	184	10	194

Error

5.7b

Counts

194 → 10

Alt Table

Status	Error	Program
	35.1b	(.f64 -1/2 (/.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
	45.9b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	58.4b	(.f64 -1/2 (log.f64 (exp.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4))))) a))))
	39.8b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	55.4b	(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
✓	35.1b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	46.5b	(.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 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))))
	45.1b	(.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))
	50.0b	(.f64 -1/2 (.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))) (sqrt.f64 a))))
▶	34.8b	(.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)))

Compiler

Compiled 5229 to 3155 computations (39.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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))
✓	0.2b	(.f64 c (.f64 a -4))
✓	0.7b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))
✓	14.2b	(sqrt.f64 (.f64 c (.f64 a -4)))

series412.0ms (5.4%)

Counts

4 → 52

Calls

4 calls:

207.0ms	(.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))
177.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))
23.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
5.0ms	(.f64 c (.f64 a -4))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
26×	`associate-r_binary64`
25×	`times-frac_binary64`
22×	`sqrt-prod_binary64`

Counts

4 → 109

Calls

4 calls:

12.0ms	(.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))
4.0ms	(.f64 c (.f64 a -4))
3.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
2.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))

simplify119.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

857×	`associate-/r*_binary64`
589×	`fma-def_binary64`
185×	`associate-/l/_binary64`
173×	`associate-l_binary64`
172×	`associate-r_binary64`

Counts

161 → 198

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	4186
1	605	3696
2	2033	3517
3	4832	3513
4	5083	3513

prune306.0ms (4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	294	2	296
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	297	9	306

Error

5.7b

Counts

306 → 9

Alt Table

Status	Error	Program
	35.1b	(.f64 -1/2 (/.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
	45.9b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	49.8b	(.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 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4)))))) a)))
	55.4b	(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
▶	35.0b	(.f64 -1/2 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a))))))) 3) (/.f64 (sqrt.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))) a)))
✓	35.1b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	39.8b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	45.1b	(.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))
	50.0b	(.f64 -1/2 (.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))) (sqrt.f64 a))))

Compiler

Compiled 11252 to 7388 computations (34.3% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.7b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))
	0.7b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))
	14.2b	(sqrt.f64 (.f64 c (.f64 a -4)))
✓	14.2b	(sqrt.f64 (.f64 -4 (.f64 c a)))

series162.0ms (2.1%)

Counts

2 → 14

Calls

2 calls:

142.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a)))))
20.0ms	(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 (0.7%)

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

prune116.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	123	9	132

Error

5.7b

Counts

132 → 9

Alt Table

Status	Error	Program
▶	35.1b	(.f64 -1/2 (/.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
	45.9b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	49.8b	(.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 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4)))))) a)))
	55.4b	(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
✓	35.0b	(.f64 -1/2 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a))))))) 3) (/.f64 (sqrt.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))) a)))
✓	35.1b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	39.8b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	45.1b	(.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))
	50.0b	(.f64 -1/2 (.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))) (sqrt.f64 a))))

Compiler

Compiled 5363 to 3634 computations (32.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	0.7b	(cbrt.f64 a)
	0.7b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))
	14.2b	(sqrt.f64 (.f64 c (.f64 a -4)))

series77.0ms (1%)

Counts

2 → 24

Calls

2 calls:

41.0ms	(cbrt.f64 a)
37.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`
9×	`pow1_binary64`

Counts

2 → 55

Calls

2 calls:

4.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
1.0ms	(cbrt.f64 a)

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

577×	`distribute-rgt-in_binary64`
561×	`log-prod_binary64`
538×	`distribute-lft-in_binary64`
525×	`unswap-sqr_binary64`
384×	`fma-def_binary64`

Counts

79 → 74

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	58	610
1	98	554
2	296	516
3	769	502
4	1799	410
5	4642	410
6	4805	410

prune115.0ms (1.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	177	11	188

Error

3.7b

Counts

188 → 11

Alt Table

Status	Error	Program
✓	35.1b	(.f64 -1/2 (/.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
	45.9b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	49.8b	(.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 (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4)))))) a)))
	46.3b	(.f64 -1/2 (/.f64 (/.f64 (.f64 b 2) (*.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
	55.4b	(*.f64 -1/2 (/.f64 (+.f64 b (neg.f64 b)) a))
✓	35.0b	(.f64 -1/2 (.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 -4 (.f64 c a))))))) 3) (/.f64 (sqrt.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))) a)))
✓	35.1b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	39.8b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	45.1b	(.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))
	47.5b	(.f64 -1/2 (/.f64 (/.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 -4 a))))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (cbrt.f64 a)))
	50.0b	(.f64 -1/2 (.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))) (sqrt.f64 a))))

Compiler

Compiled 5101 to 2693 computations (47.2% saved)

regimes2.6s (34%)

Accuracy

Total 7.5b remaining (69.6%)

Threshold costs 0b (0%)

Counts

157 → 3

Compiler

Compiled 17996 to 12410 computations (31% saved)

bsearch72.0ms (0.9%)

Steps

Iters	Range		Point
9	724.6084550517913	2837428590537.335	2768977415584.8457
10	-4.0704794903772303e-60	-7.103613424894419e-71	-1.99798746565671e-63

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	54
1	33	54
2	33	54

end1.0ms (0%)

Compiler: Compiled 40 to 27 computations (32.5% saved)

sample1.7s (22.2%)

Algorithm

1×

intervals

Results

366.0ms	1148×	body	2048	valid
359.0ms	5131×	body	128	valid
195.0ms	768×	body	1024	valid
159.0ms	402×	body	4096	valid
72.0ms	365×	body	512	valid
43.0ms	686×	body	128	nan
29.0ms	430×	body	128	invalid
23.0ms	186×	body	256	valid

Compiler

Compiled 297 to 204 computations (31.3% saved)

Details

analyze936.0ms (12.3%)

sample202.0ms (2.7%)

simplify144.0ms (1.9%)

prune3.0ms (0%)

localize9.0ms (0.1%)

series193.0ms (2.5%)

rewrite13.0ms (0.2%)

simplify85.0ms (1.1%)

prune144.0ms (1.9%)

localize11.0ms (0.1%)

series412.0ms (5.4%)

rewrite34.0ms (0.5%)

simplify119.0ms (1.6%)

prune306.0ms (4%)

localize19.0ms (0.3%)

series162.0ms (2.1%)

rewrite6.0ms (0.1%)

simplify53.0ms (0.7%)

prune116.0ms (1.5%)

localize12.0ms (0.2%)

series77.0ms (1%)

rewrite7.0ms (0.1%)

simplify65.0ms (0.9%)

prune115.0ms (1.5%)

regimes2.6s (34%)

bsearch72.0ms (0.9%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.7s (22.2%)

Profiling