Details

analyze129.0ms (2.1%)

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)

sample1.9s (31.9%)

Results

1.7s	8256×	body	128	valid
44.0ms	228×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify198.0ms (3.3%)

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

prune6.0ms (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)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
✓	0.2b	(.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))

series66.0ms (1.1%)

Counts

4 → 48

Calls

4 calls:

42.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
14.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
8.0ms	(*.f64 3 (sqrt.f64 x))
2.0ms	(/.f64 1 (*.f64 x 9))

rewrite56.0ms (0.9%)

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:

21.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
6.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
6.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(/.f64 1 (*.f64 x 9))

simplify112.0ms (1.9%)

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

prune375.0ms (6.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	162	9	171
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	163	10	173

Error

0.0b

Counts

173 → 10

Alt Table

Status	Error	Program
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
	27.7b	(.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))))
	34.9b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (cbrt.f64 (.f64 (.f64 (+.f64 y (/.f64 1 (.f64 x 9))) (+.f64 y (/.f64 1 (.f64 x 9)))) (+.f64 y (/.f64 1 (*.f64 x 9))))) 1))
	16.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 1 (sqrt.f64 (+.f64 (/.f64 1/9 x) y)))) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) 1))
▶	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	0.7b	(.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))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))) (cbrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))))
	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))
	19.8b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 3 (sqrt.f64 x))) (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.9b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))

Compiler

Compiled 4397 to 3310 computations (24.7% saved)

localize21.0ms (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)))

series40.0ms (0.7%)

Counts

3 → 0

Calls

3 calls:

16.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
16.0ms	(*.f64 y (sqrt.f64 x))
8.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

rewrite32.0ms (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:

10.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
7.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
6.0ms	(*.f64 y (sqrt.f64 x))

simplify149.0ms (2.5%)

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

prune299.0ms (4.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	138	11	149

Error

0.0b

Counts

149 → 11

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))
	34.9b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (cbrt.f64 (.f64 (.f64 (+.f64 y (/.f64 1 (.f64 x 9))) (+.f64 y (/.f64 1 (.f64 x 9)))) (+.f64 y (/.f64 1 (*.f64 x 9))))) 1))
	16.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 1 (sqrt.f64 (+.f64 (/.f64 1/9 x) y)))) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) 1))
	0.9b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.5b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 (sqrt.f64 (/.f64 1/3 (sqrt.f64 x))) (sqrt.f64 (/.f64 1/3 (sqrt.f64 x))))) (.f64 3 (sqrt.f64 x)))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
	0.7b	(.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))
	1.4b	(.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))
	19.8b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 3 (sqrt.f64 x))) (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.7b	(-.f64 (+.f64 (.f64 3 (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 x))) (cbrt.f64 (.f64 y (sqrt.f64 x)))) (cbrt.f64 (.f64 y (sqrt.f64 x))))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	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)))

Compiler

Compiled 3807 to 2441 computations (35.9% saved)

localize17.0ms (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))
✓	0.3b	(/.f64 1/3 (sqrt.f64 x))

series18.0ms (0.3%)

Counts

1 → 0

Calls

1 calls:

18.0ms

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

rewrite8.0ms (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:

5.0ms

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

simplify118.0ms (2%)

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

prune282.0ms (4.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	132	10	142

Error

0.0b

Counts

142 → 10

Alt Table

Status	Error	Program
	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1 (/.f64 (sqrt.f64 x) 1/3))) (*.f64 3 (sqrt.f64 x)))
	34.9b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (cbrt.f64 (.f64 (.f64 (+.f64 y (/.f64 1 (.f64 x 9))) (+.f64 y (/.f64 1 (.f64 x 9)))) (+.f64 y (/.f64 1 (*.f64 x 9))))) 1))
	16.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 1 (sqrt.f64 (+.f64 (/.f64 1/9 x) y)))) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) 1))
▶	0.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 (sqrt.f64 x) y) (cbrt.f64 3))) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))
	0.7b	(.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))
	1.4b	(.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))
	19.8b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 3 (sqrt.f64 x))) (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.7b	(-.f64 (+.f64 (.f64 3 (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 x))) (cbrt.f64 (.f64 y (sqrt.f64 x)))) (cbrt.f64 (.f64 y (sqrt.f64 x))))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	0.9b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))

Compiler

Compiled 3324 to 1869 computations (43.8% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series50.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

26.0ms	(.f64 (.f64 (sqrt.f64 x) y) (cbrt.f64 3))
23.0ms	(*.f64 (sqrt.f64 x) y)

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`associate-r_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`associate-l_binary64`

Counts

2 → 47

Calls

2 calls:

9.0ms	(.f64 (.f64 (sqrt.f64 x) y) (cbrt.f64 3))
6.0ms	(*.f64 (sqrt.f64 x) y)

simplify132.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

610×	`associate-/l*_binary64`
550×	`log-div_binary64`
470×	`times-frac_binary64`
369×	`*-commutative_binary64`
314×	`associate-/r*_binary64`

Counts

71 → 69

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	769
1	138	709
2	461	709
3	609	703
4	751	703
5	992	703
6	1732	703
7	3403	703
8	4736	703
9	5052	703

prune329.0ms (5.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	139	10	149

Error

0.0b

Counts

149 → 10

Alt Table

Status	Error	Program
	0.3b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 (.f64 (sqrt.f64 x) y) (cbrt.f64 (sqrt.f64 3))) (cbrt.f64 (sqrt.f64 3)))) (/.f64 1/3 (sqrt.f64 x))) (.f64 3 (sqrt.f64 x)))
	0.4b	(*.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 (/.f64 (sqrt.f64 x) 1/3))) (*.f64 3 (sqrt.f64 x)))
	16.9b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (+.f64 1 (sqrt.f64 (+.f64 (/.f64 1/9 x) y)))) (-.f64 (sqrt.f64 (+.f64 y (/.f64 1 (.f64 x 9)))) 1))
✓	0.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (.f64 (sqrt.f64 x) y) (cbrt.f64 3))) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))
	0.7b	(.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))
	1.4b	(.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))
	19.8b	(.f64 (cbrt.f64 (.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 3 (sqrt.f64 x))) (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.7b	(-.f64 (+.f64 (.f64 3 (.f64 (.f64 (cbrt.f64 (.f64 y (sqrt.f64 x))) (cbrt.f64 (.f64 y (sqrt.f64 x)))) (cbrt.f64 (.f64 y (sqrt.f64 x))))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))
	0.9b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))

Compiler

Compiled 4213 to 2765 computations (34.4% saved)

regimes1.3s (21.1%)

Accuracy

Total 0.3b remaining (87.2%)

Threshold costs 0.3b (87.2%)

Counts

202 → 1

Compiler

Compiled 13478 to 10166 computations (24.6% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	22	25
2	30	25
3	34	25
4	37	25
5	38	25
6	37	25

end336.0ms (5.6%)

Compiler: Compiled 283 to 206 computations (27.2% saved)

Details

analyze129.0ms (2.1%)

sample1.9s (31.9%)

simplify198.0ms (3.3%)

prune6.0ms (0.1%)

localize16.0ms (0.3%)

series66.0ms (1.1%)

rewrite56.0ms (0.9%)

simplify112.0ms (1.9%)

prune375.0ms (6.2%)

localize21.0ms (0.3%)

series40.0ms (0.7%)

rewrite32.0ms (0.5%)

simplify149.0ms (2.5%)

prune299.0ms (4.9%)

localize17.0ms (0.3%)

series18.0ms (0.3%)

rewrite8.0ms (0.1%)

simplify118.0ms (2%)

prune282.0ms (4.7%)

localize24.0ms (0.4%)

series50.0ms (0.8%)

rewrite18.0ms (0.3%)

simplify132.0ms (2.2%)

prune329.0ms (5.5%)

regimes1.3s (21.1%)

simplify5.0ms (0.1%)

end336.0ms (5.6%)

Profiling