Details

analyze51.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
50%	25%	25.1%	4
50%	25%	25.1%	5
50%	12.5%	37.6%	6
50%	12.5%	37.6%	7
50%	6.2%	43.8%	8
50%	6.2%	43.8%	9
50%	3.1%	46.9%	10
50%	3.1%	46.9%	11
50%	1.6%	48.5%	12
50%	1.6%	48.5%	13
50%	0.8%	49.3%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.1s (25.6%)

Results

965.0ms	8256×	body	128	valid
14.0ms	133×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify249.0ms (5.6%)

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

prune7.0ms (0.2%)

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
▶	0.3b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.4b	(*.f64 (sqrt.f64 x) (fma.f64 3 (+.f64 y (/.f64 1/9 x)) -3))

Compiler

Compiled 85 to 66 computations (22.4% saved)

localize17.0ms (0.4%)

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))

series72.0ms (1.6%)

Counts

4 → 48

Calls

4 calls:

47.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
11.0ms	(*.f64 3 (sqrt.f64 x))
8.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
6.0ms	(/.f64 1 (*.f64 x 9))

rewrite38.0ms (0.8%)

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

simplify119.0ms (2.7%)

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

prune309.0ms (6.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	161	10	171
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	163	10	173

Error

0.0b

Counts

173 → 10

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.7b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.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 (/.f64 1 x) 9)) 1))
	20.6b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (cbrt.f64 (.f64 (.f64 (/.f64 1 (.f64 x 9)) (/.f64 1 (.f64 x 9))) (/.f64 1 (*.f64 x 9))))) 1))
	0.6b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
	0.6b	(.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))
	17.1b	(.f64 (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.8b	(.f64 (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
▶	0.3b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 3 (sqrt.f64 x)))

Compiler

Compiled 4313 to 3260 computations (24.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series35.0ms (0.8%)

Counts

3 → 0

Calls

3 calls:

17.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
11.0ms	(*.f64 y (sqrt.f64 x))
8.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

rewrite19.0ms (0.4%)

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:

7.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
4.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
4.0ms	(*.f64 y (sqrt.f64 x))

simplify156.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

81 → 115

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

prune233.0ms (5.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	140	10	150

Error

0.0b

Counts

150 → 10

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.7b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	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 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.6b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
	8.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3)))
	0.4b	(-.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))))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
▶	0.3b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))

Compiler

Compiled 3727 to 2402 computations (35.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series16.0ms (0.4%)

Counts

1 → 0

Calls

1 calls:

16.0ms

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

rewrite5.0ms (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))

simplify112.0ms (2.5%)

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

prune236.0ms (5.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	132	10	142

Error

0.0b

Counts

142 → 10

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.7b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	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 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.6b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
▶	0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
	8.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3)))
	0.4b	(-.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))))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
✓	0.3b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))

Compiler

Compiled 3274 to 1851 computations (43.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series60.0ms (1.3%)

Counts

4 → 48

Calls

4 calls:

30.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
21.0ms	(*.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))
7.0ms	(+.f64 (-.f64 (/.f64 1/9 x) 1) y)
2.0ms	(/.f64 1/9 x)

rewrite88.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-sqr-sqrt_binary64`
66×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
43×	`associate-+l+_binary64`
39×	`prod-diff_binary64`

Counts

4 → 155

Calls

4 calls:

23.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
20.0ms	(*.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))
17.0ms	(+.f64 (-.f64 (/.f64 1/9 x) 1) y)
3.0ms	(/.f64 1/9 x)

simplify124.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

922×	`distribute-rgt-in_binary64`
905×	`distribute-lft-in_binary64`
285×	`fma-def_binary64`
119×	`associate-l_binary64`
117×	`associate-r_binary64`

Counts

203 → 220

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	2465
1	382	2234
2	1227	2200
3	5247	2200

prune384.0ms (8.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	220	10	230

Error

0.0b

Counts

230 → 10

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (.f64 3 (sqrt.f64 x)) (.f64 (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1)))) (cbrt.f64 (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.7b	(.f64 (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 3) (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	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 (sqrt.f64 (.f64 3 (sqrt.f64 x))) (sqrt.f64 (.f64 3 (sqrt.f64 x)))) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
	0.6b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
✓	0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 (-.f64 (/.f64 1/9 x) 1) y)))
	8.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (cbrt.f64 (pow.f64 (.f64 3 (sqrt.f64 x)) 3)))
	0.4b	(-.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))))
	0.4b	(.f64 (.f64 3 (sqrt.f64 x)) (+.f64 (-.f64 (/.f64 1/9 x) 1) y))
✓	0.3b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))

Compiler

Compiled 5154 to 3795 computations (26.4% saved)

regimes796.0ms (17.7%)

Accuracy

Total 0.3b remaining (89.4%)

Threshold costs 0.3b (89.4%)

Counts

161 → 1

Compiler

Compiled 10211 to 7960 computations (22% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-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	16	28
1	30	28
2	37	28
3	41	28
4	44	28
5	45	28
6	43	28

end178.0ms (4%)

Compiler: Compiled 264 to 205 computations (22.3% saved)

Details

analyze51.0ms (1.1%)

sample1.1s (25.6%)

simplify249.0ms (5.6%)

prune7.0ms (0.2%)

localize17.0ms (0.4%)

series72.0ms (1.6%)

rewrite38.0ms (0.8%)

simplify119.0ms (2.7%)

prune309.0ms (6.9%)

localize10.0ms (0.2%)

series35.0ms (0.8%)

rewrite19.0ms (0.4%)

simplify156.0ms (3.5%)

prune233.0ms (5.2%)

localize10.0ms (0.2%)

series16.0ms (0.4%)

rewrite5.0ms (0.1%)

simplify112.0ms (2.5%)

prune236.0ms (5.3%)

localize8.0ms (0.2%)

series60.0ms (1.3%)

rewrite88.0ms (2%)

simplify124.0ms (2.8%)

prune384.0ms (8.6%)

regimes796.0ms (17.7%)

simplify5.0ms (0.1%)

end178.0ms (4%)

Profiling