Details

analyze81.0ms (2.5%)

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)

sample1.1s (34.2%)

Results

972.0ms	8256×	body	128	valid
22.0ms	188×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify179.0ms (5.4%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(*.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)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series32.0ms (1%)

Counts

4 → 48

Calls

4 calls:

21.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
5.0ms	(*.f64 3 (sqrt.f64 x))
4.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
1.0ms	(/.f64 1 (*.f64 x 9))

rewrite32.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
30×	`prod-diff_binary64`
29×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64`

Counts

4 → 140

Calls

4 calls:

12.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
4.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
3.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(/.f64 1 (*.f64 x 9))

simplify69.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

625×	`times-frac_binary64`
456×	`distribute-rgt-in_binary64`
422×	`distribute-lft-in_binary64`
305×	`fma-def_binary64`
289×	`associate-/l*_binary64`

Counts

188 → 171

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	2841
1	412	2251
2	1241	2225
3	5098	2225

prune196.0ms (6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	161	10	171
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	162	11	173

Error

0.0b

Counts

173 → 11

Alt Table

Status	Error	Program
	27.9b	(.f64 (sqrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))) (sqrt.f64 (.f64 (*.f64 3 (sqrt.f64 x)) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))))
▶	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	29.8b	(/.f64 (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (.f64 (+.f64 y (/.f64 1 (.f64 x 9))) (+.f64 y (/.f64 1 (.f64 x 9)))) (.f64 1 1))) (+.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.8b	(.f64 (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (*.f64 (sqrt.f64 (/.f64 1/9 x)) (sqrt.f64 (/.f64 1/9 x)))) 1))
	1.0b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.6b	(.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.5b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
	22.1b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 3 3) 3) (.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	1.4b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 3 (sqrt.f64 x))) (cbrt.f64 (.f64 3 (sqrt.f64 x)))) (cbrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.8b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 x 9))) (cbrt.f64 (/.f64 1 (.f64 x 9)))) (cbrt.f64 (/.f64 1 (*.f64 x 9))))) 1))

Compiler

Compiled 4413 to 3334 computations (24.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series24.0ms (0.7%)

Counts

3 → 0

Calls

3 calls:

10.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
9.0ms	(*.f64 y (sqrt.f64 x))
5.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
23×	`associate-r_binary64`
20×	`sqrt-prod_binary64`
17×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`

Counts

3 → 81

Calls

3 calls:

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

simplify103.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

923×	`fma-def_binary64`
458×	`unswap-sqr_binary64`
457×	`associate-l_binary64`
344×	`*-commutative_binary64`
324×	`associate-/r*_binary64`

Counts

81 → 114

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	112	894
1	200	843
2	485	842
3	1076	842
4	1485	842
5	2218	801
6	2929	801
7	3312	801
8	4823	801
9	4913	801

prune157.0ms (4.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	134	5	139
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	140	10	150

Error

0.0b

Counts

150 → 10

Alt Table

Status	Error	Program
	0.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y (sqrt.f64 x)))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	0.6b	(.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	12.8b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (cbrt.f64 (/.f64 1/27 (.f64 x (sqrt.f64 x))))) (.f64 3 (sqrt.f64 x)))
	0.5b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
▶	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))
	0.5b	(-.f64 (+.f64 (.f64 3 (.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (*.f64 3 (sqrt.f64 x)))
	0.8b	(.f64 (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	1.0b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	22.1b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 3 3) 3) (.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (*.f64 3 (sqrt.f64 x)))

Compiler

Compiled 3703 to 2373 computations (35.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series10.0ms (0.3%)

Counts

1 → 0

Calls

1 calls:

10.0ms

(/.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))

simplify96.0ms (2.9%)

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

prune139.0ms (4.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	131	10	141

Error

0.0b

Counts

141 → 10

Alt Table

Status	Error	Program
▶	0.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y (sqrt.f64 x)))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	0.6b	(.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	12.8b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (cbrt.f64 (/.f64 1/27 (.f64 x (sqrt.f64 x))))) (.f64 3 (sqrt.f64 x)))
	0.5b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
✓	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))
	0.5b	(-.f64 (+.f64 (.f64 3 (.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (*.f64 3 (sqrt.f64 x)))
	0.8b	(.f64 (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	1.0b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	22.1b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 3 3) 3) (.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (*.f64 3 (sqrt.f64 x)))

Compiler

Compiled 3252 to 1825 computations (43.9% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series17.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

17.0ms

(*.f64 (cbrt.f64 3) (*.f64 y (sqrt.f64 x)))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`associate-l_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
4×	`add-cbrt-cube_binary64`
3×	`cbrt-prod_binary64`

Counts

1 → 23

Calls

1 calls:

5.0ms

(*.f64 (cbrt.f64 3) (*.f64 y (sqrt.f64 x)))

simplify78.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

705×	`log-div_binary64`
648×	`associate-/l*_binary64`
426×	`associate-l_binary64`
404×	`cube-div_binary64`
370×	`*-commutative_binary64`

Counts

35 → 35

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	469
1	92	421
2	299	421
3	802	415
4	966	415
5	1136	415
6	1401	415
7	1874	415
8	3023	415
9	4772	415
10	5064	415

prune182.0ms (5.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	146	10	156

Error

0.0b

Counts

156 → 10

Alt Table

Status	Error	Program
✓	0.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (.f64 y (sqrt.f64 x)))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	0.6b	(.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	12.8b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (cbrt.f64 (/.f64 1/27 (.f64 x (sqrt.f64 x))))) (.f64 3 (sqrt.f64 x)))
	0.5b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
✓	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))
	0.5b	(-.f64 (+.f64 (.f64 3 (.f64 (.f64 y (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x)))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (*.f64 3 (sqrt.f64 x)))
	0.8b	(.f64 (.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	1.0b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	22.1b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 3 3) 3) (.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (*.f64 3 (sqrt.f64 x)))

Compiler

Compiled 4663 to 3352 computations (28.1% saved)

regimes544.0ms (16.5%)

Accuracy

Total 0.3b remaining (89.1%)

Threshold costs 0.3b (89.1%)

Counts

160 → 1

Compiler

Compiled 9893 to 7701 computations (22.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	16	19
2	15	19

end154.0ms (4.7%)

Compiler: Compiled 253 to 192 computations (24.1% saved)

Details

analyze81.0ms (2.5%)

sample1.1s (34.2%)

simplify179.0ms (5.4%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series32.0ms (1%)

rewrite32.0ms (1%)

simplify69.0ms (2.1%)

prune196.0ms (6%)

localize11.0ms (0.3%)

series24.0ms (0.7%)

rewrite18.0ms (0.5%)

simplify103.0ms (3.1%)

prune157.0ms (4.8%)

localize9.0ms (0.3%)

series10.0ms (0.3%)

rewrite4.0ms (0.1%)

simplify96.0ms (2.9%)

prune139.0ms (4.2%)

localize14.0ms (0.4%)

series17.0ms (0.5%)

rewrite6.0ms (0.2%)

simplify78.0ms (2.4%)

prune182.0ms (5.5%)

regimes544.0ms (16.5%)

simplify2.0ms (0.1%)

end154.0ms (4.7%)

Profiling