Details

analyze65.0ms (1.9%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample139.0ms (4.2%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
0.0ms	3×	body	128	invalid
0.0ms	2×	body	128	nan

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify185.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

1205×	`fma-neg_binary64`
900×	`fma-def_binary64`
326×	`associate-/l*_binary64`
318×	`cancel-sign-sub-inv_binary64`
290×	`distribute-rgt-neg-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	28	18
2	68	18
3	145	16
4	257	16
5	411	16
6	861	16
7	1371	16
8	2386	16
9	2493	16
10	2675	16
11	2607	16
12	2581	16
13	2581	16
14	3531	16
15	3364	16
16	3364	16
17	3364	16
18	3364	16
19	3171	16

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))

Compiler

Compiled 85 to 66 computations (22.4% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (/.f64 1/9 x))
✓	0.2b	(fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)
✓	0.3b	(/.f64 1/9 x)
✓	0.3b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))

series34.0ms (1%)

Counts

4 → 60

Calls

4 calls:

22.0ms	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
6.0ms	(fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)
4.0ms	(+.f64 y (/.f64 1/9 x))
1.0ms	(/.f64 1/9 x)

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 82

Calls

4 calls:

7.0ms	(+.f64 y (/.f64 1/9 x))
4.0ms	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
2.0ms	(/.f64 1/9 x)
0.0ms	(fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)

simplify89.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

558×	`associate-/l*_binary64`
373×	`fma-neg_binary64`
355×	`associate-/l/_binary64`
311×	`associate-/r*_binary64`
275×	`associate-l_binary64`

Counts

142 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	138	1789
1	283	1627
2	757	1625
3	2493	1625
4	4739	1625
5	4915	1625

prune133.0ms (4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	122	9	131
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	123	10	133

Error

Counts

133 → 10

Alt Table

Status	Error	Program
	34.5b	(.f64 (sqrt.f64 x) (cbrt.f64 (.f64 (*.f64 (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))))
	0.4b	(.f64 (sqrt.f64 x) (-.f64 (+.f64 (.f64 3 y) (*.f64 1/3 (/.f64 1 x))) 3))
	0.5b	(.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (.f64 (*.f64 (cbrt.f64 1/9) (cbrt.f64 1/9)) (/.f64 (cbrt.f64 1/9) x))) -3))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))) (cbrt.f64 (.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)))) (cbrt.f64 (*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))))
▶	0.3b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	1.0b	(.f64 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 (sqrt.f64 (cbrt.f64 x)) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)))
	0.6b	(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (-.f64 (fma.f64 3 y (/.f64 1/3 x)) 3) (sqrt.f64 (sqrt.f64 x))))
	1.2b	(.f64 (.f64 (sqrt.f64 x) (*.f64 (cbrt.f64 (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)) (cbrt.f64 (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)))) (cbrt.f64 (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 (/.f64 1/9 (sqrt.f64 x)) (sqrt.f64 x))) -3))

Compiler

Compiled 2632 to 1792 computations (31.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 y (sqrt.f64 x))
✓	0.3b	(.f64 3 (.f64 y (sqrt.f64 x)))
✓	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.4b	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

series39.0ms (1.2%)

Counts

4 → 0

Calls

4 calls:

14.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
10.0ms	(*.f64 y (sqrt.f64 x))
8.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
6.0ms	(*.f64 3 (sqrt.f64 x))

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
29×	`associate-r_binary64`
24×	`sqrt-prod_binary64`
21×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`

Counts

4 → 105

Calls

4 calls:

6.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
5.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
4.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(*.f64 y (sqrt.f64 x))

simplify117.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

487×	`associate-l_binary64`
462×	`unswap-sqr_binary64`
438×	`sqr-pow_binary64`
341×	`*-commutative_binary64`
331×	`associate-r_binary64`

Counts

105 → 150

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	131	1109
1	241	1052
2	551	1051
3	1139	1051
4	1559	1051
5	2297	1010
6	2970	1010
7	3518	1010
8	4808	1010
9	4920	1010

prune171.0ms (5.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	151	9	160

Error

Counts

160 → 9

Alt Table

Status	Error	Program
	0.6b	(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (-.f64 (fma.f64 3 y (/.f64 1/3 x)) 3) (sqrt.f64 (sqrt.f64 x))))
	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x))))
	34.5b	(.f64 (sqrt.f64 x) (cbrt.f64 (.f64 (*.f64 (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))))
	0.4b	(.f64 (sqrt.f64 x) (-.f64 (+.f64 (.f64 3 y) (*.f64 1/3 (/.f64 1 x))) 3))
	0.5b	(.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (.f64 (*.f64 (cbrt.f64 1/9) (cbrt.f64 1/9)) (/.f64 (cbrt.f64 1/9) x))) -3))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))) (cbrt.f64 (.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)))) (cbrt.f64 (*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))))
	0.5b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 (*.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
▶	0.3b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))

Compiler

Compiled 3934 to 2515 computations (36.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 y (sqrt.f64 x))
	0.3b	(.f64 3 (.f64 y (sqrt.f64 x)))
	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.4b	(/.f64 1/3 (sqrt.f64 x))

series17.0ms (0.5%)

Counts

1 → 0

Calls

1 calls:

17.0ms

(/.f64 1/3 (sqrt.f64 x))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`times-frac_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
12×	`sqrt-prod_binary64`

Counts

1 → 41

Calls

1 calls:

3.0ms

(/.f64 1/3 (sqrt.f64 x))

simplify94.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1051×	`fma-neg_binary64`
416×	`unswap-sqr_binary64`
375×	`associate-/l/_binary64`
356×	`times-frac_binary64`
325×	`associate-/l*_binary64`

Counts

41 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	68	540
1	101	514
2	165	514
3	221	514
4	353	514
5	469	514
6	645	514
7	1189	514
8	2252	514
9	2826	514
10	3214	514
11	4235	514
12	4855	514

prune171.0ms (5.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	143	8	151

Error

Counts

151 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (-.f64 (fma.f64 3 y (/.f64 1/3 x)) 3) (sqrt.f64 (sqrt.f64 x))))
	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x))))
	0.5b	(.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (.f64 (*.f64 (cbrt.f64 1/9) (cbrt.f64 1/9)) (/.f64 (cbrt.f64 1/9) x))) -3))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.5b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
	34.5b	(.f64 (sqrt.f64 x) (cbrt.f64 (.f64 (*.f64 (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))))
▶	0.3b	(-.f64 (+.f64 (.f64 (.f64 3 y) (sqrt.f64 x)) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))) (cbrt.f64 (.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)))) (cbrt.f64 (*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))))

Compiler

Compiled 3443 to 1914 computations (44.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 3 y) (sqrt.f64 x)) (/.f64 1/3 (sqrt.f64 x)))
✓	0.3b	(.f64 (.f64 3 y) (sqrt.f64 x))
	0.3b	(*.f64 3 (sqrt.f64 x))
	0.4b	(/.f64 1/3 (sqrt.f64 x))

series32.0ms (1%)

Counts

2 → 24

Calls

2 calls:

19.0ms	(+.f64 (.f64 (.f64 3 y) (sqrt.f64 x)) (/.f64 1/3 (sqrt.f64 x)))
13.0ms	(.f64 (.f64 3 y) (sqrt.f64 x))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`associate-r_binary64`
4×	`*-un-lft-identity_binary64`

Counts

2 → 37

Calls

2 calls:

7.0ms	(+.f64 (.f64 (.f64 3 y) (sqrt.f64 x)) (/.f64 1/3 (sqrt.f64 x)))
5.0ms	(.f64 (.f64 3 y) (sqrt.f64 x))

simplify103.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

585×	`fma-neg_binary64`
511×	`cancel-sign-sub-inv_binary64`
299×	`distribute-rgt-neg-in_binary64`
281×	`*-commutative_binary64`
251×	`distribute-rgt-out_binary64`

Counts

61 → 57

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	78	863
1	200	825
2	665	808
3	1472	806
4	3102	796
5	4149	796
6	4762	796
7	4862	796

prune151.0ms (4.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	135	8	143

Error

Counts

143 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (-.f64 (fma.f64 3 y (/.f64 1/3 x)) 3) (sqrt.f64 (sqrt.f64 x))))
	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x))))
	0.5b	(.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (.f64 (*.f64 (cbrt.f64 1/9) (cbrt.f64 1/9)) (/.f64 (cbrt.f64 1/9) x))) -3))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.5b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
	34.5b	(.f64 (sqrt.f64 x) (cbrt.f64 (.f64 (*.f64 (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))))
✓	0.3b	(-.f64 (+.f64 (.f64 (.f64 3 y) (sqrt.f64 x)) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))) (cbrt.f64 (.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3)))) (cbrt.f64 (*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))))

Compiler

Compiled 3179 to 1879 computations (40.9% saved)

regimes846.0ms (25.3%)

Accuracy

Total 0.3b remaining (89.8%)

Threshold costs 0.3b (89.8%)

Counts

225 → 1

Compiler

Compiled 14192 to 10423 computations (26.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	27	25
2	38	25
3	41	25
4	44	25
5	45	25
6	42	25

end1.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

sample858.0ms (25.7%)

Algorithm

1×

intervals

Results

499.0ms	8000×	body	128	valid
7.0ms	133×	body	128	nan
5.0ms	74×	body	128	invalid

Compiler

Compiled 231 to 174 computations (24.7% saved)

Details

analyze65.0ms (1.9%)

sample139.0ms (4.2%)

simplify185.0ms (5.5%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series34.0ms (1%)

rewrite16.0ms (0.5%)

simplify89.0ms (2.7%)

prune133.0ms (4%)

localize10.0ms (0.3%)

series39.0ms (1.2%)

rewrite22.0ms (0.7%)

simplify117.0ms (3.5%)

prune171.0ms (5.1%)

localize8.0ms (0.2%)

series17.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify94.0ms (2.8%)

prune171.0ms (5.1%)

localize8.0ms (0.2%)

series32.0ms (1%)

rewrite14.0ms (0.4%)

simplify103.0ms (3.1%)

prune151.0ms (4.5%)

regimes846.0ms (25.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample858.0ms (25.7%)

Profiling