Details

analyze602.0ms (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)

sample39.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	171×	body	128	valid
8.0ms	35×	body	2048	valid
4.0ms	19×	body	1024	valid
2.0ms	8×	body	4096	valid
2.0ms	15×	body	512	valid
1.0ms	8×	body	256	valid
1.0ms	15×	body	128	nan
1.0ms	13×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify328.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1228×	`associate-/l*_binary64`
1150×	`div-sub_binary64`
630×	`distribute-rgt-in_binary64`
619×	`times-frac_binary64`
588×	`associate-/r*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	33	24
2	62	24
3	121	24
4	172	24
5	282	24
6	460	24
7	748	24
8	1084	24
9	1128	24
10	1799	24
11	2594	24
12	2001	24
13	2089	24
14	2153	24
15	2179	24
16	2431	24
17	2909	24
18	2913	24
19	2991	24
20	3053	24
21	3065	24
22	3035	24
23	3211	24
24	3211	24
25	2043	24
26	2195	24
27	2097	24
28	2107	24
29	2107	24
30	2107	24
31	2107	24
32	1834	24

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

32.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	32.8b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))

Compiler

Compiled 57 to 39 computations (31.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite169.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

32.5b

Rules

21×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
6×	`sqrt-prod_binary64` `difference-of-squares_binary64` `times-frac_binary64` `associate-/l*_binary64`

Counts

4 → 74

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 1903 to 985 computations (48.2% saved)

series243.0ms (2.8%)

Error

5.8b

Counts

4 → 71

Calls

4 calls:

61.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
54.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
51.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
47.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2955 to 2111 computations (28.6% saved)

simplify116.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

580×	`associate-/l*_binary64`
496×	`associate-/r*_binary64`
351×	`div-sub_binary64`
192×	`cancel-sign-sub-inv_binary64`
185×	`distribute-rgt-in_binary64`

Counts

145 → 93

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	203	3165
1	549	2927
2	1682	2921
3	4787	2921
4	5656	2921

prune69.0ms (0.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	84	9	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	9	94

Error

5.7b

Counts

94 → 9

Alt Table

Status	Error	Program
	44.5b	(/.f64 (sqrt.f64 (.f64 a (.f64 c -4))) (*.f64 a 2))
▶	32.9b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
	44.0b	(/.f64 (neg.f64 b) a)
	40.6b	(neg.f64 (/.f64 c b))
	33.0b	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b)) (/.f64 a (/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b)) 2)))
	44.8b	(/.f64 (/.f64 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 a c)) (.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
	34.3b	(/.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) b) (.f64 a 2))
	32.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
	49.0b	(/.f64 (-.f64 (sqrt.f64 (.f64 b b)) b) (.f64 a 2))

Compiler

Compiled 1518 to 867 computations (42.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite465.0ms (5.4%)

Algorithm

1×	rewrite-expression-head

Error

5.7b

Rules

693×	`times-frac_binary64`
439×	`add-sqr-sqrt_binary64`
364×	`*-un-lft-identity_binary64`
290×	`add-cube-cbrt_binary64`
74×	`difference-of-squares_binary64`

Counts

4 → 356

Calls

4 calls:

26.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 11060 to 6512 computations (41.1% saved)

series237.0ms (2.7%)

Error

5.7b

Counts

4 → 71

Calls

4 calls:

62.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
54.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
51.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
44.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 3153 to 2309 computations (26.8% saved)

simplify439.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

316×	`associate-/r/_binary64`
233×	`*-commutative_binary64`
208×	`neg-mul-1_binary64`
192×	`associate-*l/_binary64`
189×	`cancel-sign-sub-inv_binary64`

Counts

427 → 379

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	416	17577
1	962	16528
2	3080	16236
3	4574	16236
4	5020	16236

prune173.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	378	1	379
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	379	9	388

Error

5.7b

Counts

388 → 9

Alt Table

Status	Error	Program
	44.5b	(/.f64 (sqrt.f64 (.f64 a (.f64 c -4))) (*.f64 a 2))
✓	32.9b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
	44.0b	(/.f64 (neg.f64 b) a)
	40.6b	(neg.f64 (/.f64 c b))
	33.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2) (cbrt.f64 a)))
	44.8b	(/.f64 (/.f64 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 a c)) (.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
	34.3b	(/.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) b) (.f64 a 2))
▶	32.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
	49.0b	(/.f64 (-.f64 (sqrt.f64 (.f64 b b)) b) (.f64 a 2))

Compiler

Compiled 5071 to 2771 computations (45.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite115.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

5.7b

Rules

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

Counts

4 → 83

Calls

4 calls:

14.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
7.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2202 to 1153 computations (47.6% saved)

series239.0ms (2.8%)

Error

5.7b

Counts

4 → 71

Calls

4 calls:

65.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
55.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
50.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
42.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2955 to 2111 computations (28.6% saved)

simplify127.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

546×	`associate-/l*_binary64`
295×	`distribute-rgt-in_binary64`
285×	`distribute-lft-in_binary64`
181×	`cancel-sign-sub-inv_binary64`
156×	`distribute-rgt-neg-in_binary64`

Counts

154 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	3407
1	580	3173
2	1906	3167
3	4822	3167
4	4950	3167

prune60.0ms (0.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	91	10	101

Error

5.7b

Counts

101 → 10

Alt Table

Status	Error	Program
	44.5b	(/.f64 (sqrt.f64 (.f64 a (.f64 c -4))) (*.f64 a 2))
✓	32.9b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
	44.0b	(/.f64 (neg.f64 b) a)
	44.1b	(.f64 (.f64 b -2) (/.f64 1/2 a))
	40.6b	(neg.f64 (/.f64 c b))
▶	33.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2) (cbrt.f64 a)))
	44.8b	(/.f64 (/.f64 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 a c)) (.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
	34.3b	(/.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) b) (.f64 a 2))
✓	32.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
	49.0b	(/.f64 (-.f64 (sqrt.f64 (.f64 b b)) b) (.f64 a 2))

Compiler

Compiled 1447 to 830 computations (42.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 a)
0.7b	(cbrt.f64 a)
2.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
22.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite65.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

5.7b

Rules

13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64`

Counts

4 → 54

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
1.0ms	(cbrt.f64 a)
1.0ms	(cbrt.f64 a)

Compiler

Compiled 1712 to 795 computations (53.6% saved)

series168.0ms (1.9%)

Error

5.7b

Counts

4 → 42

Calls

4 calls:

56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
54.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
20.0ms	(cbrt.f64 a)
18.0ms	(cbrt.f64 a)

Compiler

Compiled 2821 to 1866 computations (33.9% saved)

simplify125.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

686×	`times-frac_binary64`
391×	`unswap-sqr_binary64`
246×	`associate-/l*_binary64`
227×	`associate-/r*_binary64`
216×	`*-commutative_binary64`

Counts

96 → 52

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1515
1	325	1458
2	970	1451
3	3847	1439
4	4823	1439
5	4952	1439
6	4919	1439

prune43.0ms (0.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	51	11	62

Error

5.7b

Counts

62 → 11

Alt Table

Status	Error	Program
	44.5b	(/.f64 (sqrt.f64 (.f64 a (.f64 c -4))) (*.f64 a 2))
	44.4b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (/.f64 (*.f64 b -2) 2) (cbrt.f64 a)))
	44.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (/.f64 (sqrt.f64 (.f64 a (.f64 c -4))) 2) (cbrt.f64 a)))
	32.9b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
	44.0b	(/.f64 (neg.f64 b) a)
	44.1b	(.f64 (.f64 b -2) (/.f64 1/2 a))
	40.6b	(neg.f64 (/.f64 c b))
	44.8b	(/.f64 (/.f64 (-.f64 (.f64 b b) (+.f64 (.f64 4 (.f64 a c)) (.f64 b b))) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
	34.3b	(/.f64 (-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) b) (.f64 a 2))
	32.9b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
	49.0b	(/.f64 (-.f64 (sqrt.f64 (.f64 b b)) b) (.f64 a 2))

Compiler

Compiled 1248 to 664 computations (46.8% saved)

regimes3.2s (37%)

Accuracy

Total 4.4b remaining (43.3%)

Threshold costs 0b (0%)

Compiler

Compiled 19208 to 13578 computations (29.3% saved)

bsearch49.0ms (0.6%)

Steps

Iters	Range		Point
9	1.5703880844671802e-105	2.1738535384880125e-98	7.0816198577945554e-99
3	-2.4018857695839242e+157	-2.5633663016704837e+152	-1.0804275471361773e+153

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`sub-neg_binary64` `*-commutative_binary64` `+-commutative_binary64`
7×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`
4×	`distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`
2×	`mul-1-neg_binary64` `cancel-sign-sub-inv_binary64` `distribute-neg-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	48
1	40	48
2	55	48
3	70	48
4	80	48
5	84	48
6	85	48
7	84	48

end1.0ms (0%)

Compiler: Compiled 35 to 23 computations (34.3% saved)

sample1.5s (17.5%)

Algorithm

1×

intervals

Results

288.0ms	1148×	body	2048	valid
269.0ms	5148×	body	128	valid
154.0ms	753×	body	1024	valid
130.0ms	394×	body	4096	valid
54.0ms	374×	body	512	valid
37.0ms	646×	body	128	nan
20.0ms	387×	body	128	invalid
18.0ms	183×	body	256	valid

Compiler

Compiled 255 to 172 computations (32.5% saved)

Details

analyze602.0ms (7%)

sample39.0ms (0.4%)

simplify328.0ms (3.8%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite169.0ms (2%)

series243.0ms (2.8%)

simplify116.0ms (1.3%)

prune69.0ms (0.8%)

localize12.0ms (0.1%)

rewrite465.0ms (5.4%)

series237.0ms (2.7%)

simplify439.0ms (5.1%)

prune173.0ms (2%)

localize10.0ms (0.1%)

rewrite115.0ms (1.3%)

series239.0ms (2.8%)

simplify127.0ms (1.5%)

prune60.0ms (0.7%)

localize18.0ms (0.2%)

rewrite65.0ms (0.8%)

series168.0ms (1.9%)

simplify125.0ms (1.5%)

prune43.0ms (0.5%)

regimes3.2s (37%)

bsearch49.0ms (0.6%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.5s (17.5%)

Profiling