Details

analyze63.0ms (2%)

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 (4.3%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
0.0ms	2×	body	128	nan
0.0ms	1×	body	128	invalid

Compiler

Compiled 35 to 29 computations (17.1% saved)

simplify180.0ms (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

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 (.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)

localize9.0ms (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))

series41.0ms (1.3%)

Counts

4 → 48

Calls

4 calls:

26.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
9.0ms	(*.f64 3 (sqrt.f64 x))
4.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
1.0ms	(/.f64 1 (*.f64 x 9))

rewrite34.0ms (1.1%)

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))
8.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
3.0ms	(*.f64 3 (sqrt.f64 x))
3.0ms	(/.f64 1 (*.f64 x 9))

simplify75.0ms (2.4%)

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

prune223.0ms (7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	160	11	171
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	161	12	173

Error

0.0b

Counts

173 → 12

Alt Table

Status	Error	Program
	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))
▶	0.4b	(-.f64 (+.f64 (.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))
	0.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (/.f64 1 (.f64 x 9))) 1))
	15.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (*.f64 (sqrt.f64 (+.f64 (/.f64 1/9 x) y)) (sqrt.f64 (+.f64 (/.f64 1/9 x) y))) 1))
	22.8b	(.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))
	33.5b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (log.f64 (exp.f64 (/.f64 1/9 x)))) 1))
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.7b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.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))
	28.8b	(.f64 (sqrt.f64 (.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))) (sqrt.f64 (.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 4381 to 3304 computations (24.6% saved)

localize10.0ms (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)))

series34.0ms (1.1%)

Counts

3 → 0

Calls

3 calls:

18.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
10.0ms	(*.f64 y (sqrt.f64 x))
7.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

rewrite23.0ms (0.7%)

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)))
4.0ms	(.f64 3 (.f64 y (sqrt.f64 x)))
4.0ms	(*.f64 y (sqrt.f64 x))

simplify106.0ms (3.3%)

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

prune175.0ms (5.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	140	11	151

Error

0.0b

Counts

151 → 11

Alt Table

Status	Error	Program
	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))
	0.4b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))
	0.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (/.f64 1 (.f64 x 9))) 1))
▶	0.4b	(-.f64 (+.f64 (.f64 (.f64 3 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)))
	33.5b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (log.f64 (exp.f64 (/.f64 1/9 x)))) 1))
	0.4b	(.f64 3 (.f64 (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))
	0.7b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.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))
	0.5b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 (.f64 1/3 (sqrt.f64 (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 (sqrt.f64 (/.f64 1 x))))) (*.f64 3 (sqrt.f64 x)))

Compiler

Compiled 3719 to 2391 computations (35.7% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (/.f64 1 x))
	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.3b	(.f64 (.f64 3 y) (sqrt.f64 x))
	0.4b	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

series20.0ms (0.6%)

Counts

2 → 12

Calls

2 calls:

12.0ms	(.f64 (.f64 3 y) (sqrt.f64 x))
8.0ms	(sqrt.f64 (/.f64 1 x))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 53

Calls

2 calls:

5.0ms	(.f64 (.f64 3 y) (sqrt.f64 x))
2.0ms	(sqrt.f64 (/.f64 1 x))

simplify83.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

830×	`associate-/l*_binary64`
547×	`associate-l_binary64`
491×	`unswap-sqr_binary64`
375×	`associate-r_binary64`
357×	`*-commutative_binary64`

Counts

65 → 68

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	81	648
1	141	618
2	413	618
3	1053	618
4	1251	618
5	1606	617
6	3204	617
7	4599	617
8	4866	617

prune179.0ms (5.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	147	10	157

Error

0.0b

Counts

157 → 10

Alt Table

Status	Error	Program
	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))
	0.5b	(-.f64 (+.f64 (.f64 (.f64 3 y) (sqrt.f64 x)) (.f64 1/3 (sqrt.f64 (/.f64 1 x)))) (.f64 (sqrt.f64 3) (*.f64 (sqrt.f64 x) (sqrt.f64 3))))
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
▶	0.4b	(-.f64 (+.f64 (.f64 (.f64 3 y) (sqrt.f64 x)) (/.f64 1/3 (sqrt.f64 x))) (*.f64 3 (sqrt.f64 x)))
	0.5b	(-.f64 (+.f64 (.f64 (.f64 3 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))))
	0.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.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)))
	33.5b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (log.f64 (exp.f64 (/.f64 1/9 x)))) 1))
	0.7b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.5b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 (.f64 1/3 (sqrt.f64 (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 (sqrt.f64 (/.f64 1 x))))) (*.f64 3 (sqrt.f64 x)))

Compiler

Compiled 3862 to 2638 computations (31.7% saved)

localize8.0ms (0.3%)

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 3 (sqrt.f64 x))
	0.3b	(.f64 (.f64 3 y) (sqrt.f64 x))
✓	0.4b	(/.f64 1/3 (sqrt.f64 x))

series38.0ms (1.2%)

Counts

2 → 12

Calls

2 calls:

22.0ms	(+.f64 (.f64 (.f64 3 y) (sqrt.f64 x)) (/.f64 1/3 (sqrt.f64 x)))
16.0ms	(/.f64 1/3 (sqrt.f64 x))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 55

Calls

2 calls:

8.0ms	(+.f64 (.f64 (.f64 3 y) (sqrt.f64 x)) (/.f64 1/3 (sqrt.f64 x)))
3.0ms	(/.f64 1/3 (sqrt.f64 x))

simplify94.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-neg_binary64`
378×	`associate-l_binary64`
322×	`associate-r_binary64`
289×	`distribute-rgt-in_binary64`
256×	`distribute-lft-in_binary64`

Counts

67 → 73

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	1033
1	205	989
2	553	972
3	1750	960
4	4018	960
5	4980	960
6	5040	960

prune146.0ms (4.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	129	9	138

Error

0.0b

Counts

138 → 9

Alt Table

Status	Error	Program
	0.4b	(-.f64 (+.f64 (.f64 (.f64 3 y) (sqrt.f64 x)) (/.f64 1/3 (sqrt.f64 x))) (.f64 (sqrt.f64 3) (.f64 (sqrt.f64 x) (sqrt.f64 3))))
	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)))
	0.5b	(-.f64 (+.f64 (.f64 (.f64 3 y) (sqrt.f64 x)) (/.f64 1/3 (sqrt.f64 x))) (.f64 (.f64 3 (fabs.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 x))))
	33.5b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (log.f64 (exp.f64 (/.f64 1/9 x)))) 1))
	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))
	0.7b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (fma.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (cbrt.f64 y) (/.f64 1 (.f64 x 9))) 1))
	0.4b	(.f64 3 (.f64 (sqrt.f64 x) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1)))
	0.7b	(.f64 (.f64 (.f64 3 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x))) (-.f64 (+.f64 y (/.f64 1 (.f64 x 9))) 1))
	0.5b	(-.f64 (+.f64 (.f64 3 (.f64 y (sqrt.f64 x))) (.f64 (.f64 1/3 (sqrt.f64 (sqrt.f64 (/.f64 1 x)))) (sqrt.f64 (sqrt.f64 (/.f64 1 x))))) (*.f64 3 (sqrt.f64 x)))

Compiler

Compiled 3033 to 1790 computations (41% saved)

regimes650.0ms (20.4%)

Accuracy

Total 0.3b remaining (89.4%)

Threshold costs 0.3b (89.4%)

Counts

171 → 1

Compiler

Compiled 11708 to 9189 computations (21.5% saved)

simplify3.0ms (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	14	25
1	22	25
2	33	25
3	37	25
4	40	25
5	41	25
6	39	25

end1.0ms (0%)

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

sample816.0ms (25.6%)

Algorithm

1×

intervals

Results

457.0ms	8000×	body	128	valid
7.0ms	128×	body	128	nan
4.0ms	74×	body	128	invalid

Compiler

Compiled 234 to 177 computations (24.4% saved)

Details

analyze63.0ms (2%)

sample139.0ms (4.3%)

simplify180.0ms (5.6%)

prune4.0ms (0.1%)

localize9.0ms (0.3%)

series41.0ms (1.3%)

rewrite34.0ms (1.1%)

simplify75.0ms (2.4%)

prune223.0ms (7%)

localize10.0ms (0.3%)

series34.0ms (1.1%)

rewrite23.0ms (0.7%)

simplify106.0ms (3.3%)

prune175.0ms (5.5%)

localize11.0ms (0.4%)

series20.0ms (0.6%)

rewrite10.0ms (0.3%)

simplify83.0ms (2.6%)

prune179.0ms (5.6%)

localize8.0ms (0.3%)

series38.0ms (1.2%)

rewrite13.0ms (0.4%)

simplify94.0ms (2.9%)

prune146.0ms (4.6%)

regimes650.0ms (20.4%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample816.0ms (25.6%)

Profiling