Details

analyze690.0ms (9.7%)

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)

sample3.1s (43.3%)

Results

780.0ms	5330×	body	128	valid
702.0ms	1204×	body	2048	valid
426.0ms	180×	body	256	valid
370.0ms	422×	body	4096	valid
354.0ms	769×	body	1024	valid
154.0ms	1105×	body	128	invalid
129.0ms	351×	body	512	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify146.0ms (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

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

32.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	32.5b	(.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 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))))
✓	18.7b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series201.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

88.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
52.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
46.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
14.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite17.0ms (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:

8.0ms	(/.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))

simplify99.0ms (1.4%)

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

prune156.0ms (2.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	183	10	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	183	11	194

Error

5.0b

Counts

194 → 11

Alt Table

Status	Error	Program
	38.4b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	47.0b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	34.6b	(.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))
✓	32.5b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	33.6b	(.f64 -1/2 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) (cbrt.f64 a))))
▶	32.6b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	48.1b	(.f64 -1/2 (cbrt.f64 (pow.f64 (/.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4))))) a) 3)))
	43.3b	(.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))
	43.9b	(.f64 -1/2 (/.f64 (.f64 2 (/.f64 (*.f64 c a) b)) a))
	33.5b	(.f64 -1/2 (.f64 (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (sqrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (*.f64 a -4)))))) (cbrt.f64 a))))

Compiler

Compiled 5321 to 3221 computations (39.5% 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))))
	18.7b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series74.0ms (1%)

Counts

1 → 20

Calls

1 calls:

74.0ms

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

rewrite12.0ms (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))

simplify83.0ms (1.2%)

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

prune154.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	209	9	218

Error

5.0b

Counts

218 → 9

Alt Table

Status	Error	Program
	38.4b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	47.0b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
✓	32.5b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
▶	33.6b	(.f64 -1/2 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) (cbrt.f64 a))))
✓	32.6b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	43.3b	(.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))
	43.9b	(.f64 -1/2 (/.f64 (.f64 2 (/.f64 (*.f64 c a) b)) a))
	42.1b	(.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 5759 to 3616 computations (37.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
✓	0.6b	(cbrt.f64 a)
✓	0.7b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))
✓	14.3b	(sqrt.f64 (.f64 c (.f64 a -4)))

series262.0ms (3.7%)

Counts

4 → 38

Calls

4 calls:

165.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))
40.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
36.0ms	(cbrt.f64 a)
21.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
17×	`pow1_binary64`
16×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 86

Calls

4 calls:

5.0ms	(*.f64 (cbrt.f64 a) (cbrt.f64 a))
3.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))
3.0ms	(sqrt.f64 (.f64 c (.f64 a -4)))
1.0ms	(cbrt.f64 a)

simplify104.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

920×	`fma-def_binary64`
616×	`times-frac_binary64`
326×	`associate-/l*_binary64`
259×	`associate-/r*_binary64`
254×	`fma-neg_binary64`

Counts

124 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	1568
1	335	1418
2	970	1356
3	3858	1335
4	4911	1335
5	4990	1335
6	4925	1335

prune314.0ms (4.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	319	1	320
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	320	9	329

Error

5.0b

Counts

329 → 9

Alt Table

Status	Error	Program
▶	38.4b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	47.0b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
✓	32.5b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	49.2b	(.f64 -1/2 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4)))))) (cbrt.f64 a))))
✓	32.6b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	43.3b	(.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))
	43.9b	(.f64 -1/2 (/.f64 (.f64 2 (/.f64 (*.f64 c a) b)) a))
	42.1b	(.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 17550 to 10495 computations (40.2% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (/.f64 c b))

series8.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

8.0ms

(*.f64 2 (/.f64 c b))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 34

Calls

1 calls:

5.0ms

(*.f64 2 (/.f64 c b))

simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

873×	`times-frac_binary64`
762×	`distribute-rgt-out_binary64`
407×	`associate-/l*_binary64`
338×	`associate-*l/_binary64`
306×	`*-commutative_binary64`

Counts

34 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	72	381
1	156	345
2	390	345
3	851	345
4	1890	345
5	2031	345
6	2747	345
7	3564	345
8	4507	345
9	4823	345
10	5328	345

prune29.0ms (0.4%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	40	11	51

Error

5.0b

Counts

51 → 11

Alt Table

Status	Error	Program
✓	38.4b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	47.0b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	38.5b	(.f64 -1/2 (.f64 (*.f64 2 c) (/.f64 1 b)))
	47.1b	(.f64 -1/2 (.f64 2 (-.f64 (/.f64 b a) (/.f64 c b))))
	38.8b	(.f64 -1/2 (.f64 (.f64 2 (.f64 (cbrt.f64 c) (cbrt.f64 c))) (/.f64 (cbrt.f64 c) b)))
✓	32.5b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))
	49.2b	(.f64 -1/2 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4)))))) (cbrt.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -4))))))) (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (cbrt.f64 (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -4)))))) (cbrt.f64 a))))
✓	32.6b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	43.3b	(.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))
	49.3b	(.f64 -1/2 (exp.f64 (log.f64 (.f64 2 (/.f64 c b)))))
	42.1b	(.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 772 to 470 computations (39.1% saved)

regimes1.3s (17.9%)

Accuracy

Total 4.8b remaining (47.5%)

Threshold costs 0b (0%)

Counts

98 → 3

Compiler

Compiled 9700 to 6554 computations (32.4% saved)

bsearch84.0ms (1.2%)

Steps

Iters	Range		Point
5	9.80829702453035e+40	2.2638658576504296e+41	2.231921292472624e+41
9	-1.3813457207494118e-29	-3.0714808753382253e-37	-1.0146759972633307e-36

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (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	28	60
1	37	60
2	44	60
3	48	60
4	51	60
5	52	60
6	52	60

end166.0ms (2.3%)

Compiler: Compiled 312 to 209 computations (33% saved)

Details

analyze690.0ms (9.7%)

sample3.1s (43.3%)

simplify146.0ms (2.1%)

prune4.0ms (0.1%)

localize10.0ms (0.1%)

series201.0ms (2.8%)

rewrite17.0ms (0.2%)

simplify99.0ms (1.4%)

prune156.0ms (2.2%)

localize11.0ms (0.2%)

series74.0ms (1%)

rewrite12.0ms (0.2%)

simplify83.0ms (1.2%)

prune154.0ms (2.2%)

localize16.0ms (0.2%)

series262.0ms (3.7%)

rewrite15.0ms (0.2%)

simplify104.0ms (1.5%)

prune314.0ms (4.4%)

localize5.0ms (0.1%)

series8.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify92.0ms (1.3%)

prune29.0ms (0.4%)

regimes1.3s (17.9%)

bsearch84.0ms (1.2%)

simplify4.0ms (0.1%)

end166.0ms (2.3%)

Profiling